RU2540817C1 - Chaotic oscillation generator - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: chaotic oscillation generator comprises a first bipolar element with inductive reactance, a first nonlinear impedance converter of a first type, a second bipolar element with inductive resistance, a bipolar element with capacitive resistance and two resistors.

EFFECT: wider control range of parameters of a chaotic signal by varying the configuration of the corresponding chaotic attractor.

2 cl, 24 dwg

Description

The present invention relates to radio engineering and can be used as a source of chaotic electromagnetic waves.

The known generator of chaotic oscillations (N. Inaba, T. Saito and S. Mori. Chaotic phenomena in a circuit with negative resistance and ideal swith of diodes // The transactions of IEICE, 1987, Vol. E 70, No. 8, P.744 ) containing a device with negative resistance, the first terminal of which is connected to the first terminals of the first capacitor and non-linear resistor, the second terminal is connected to the second terminal of the first capacitor and the first terminals of the second capacitor and inductive element, the second terminals of which are connected to the second terminal of the non-linear resistor.

Also known is a generator of chaotic oscillations (T. Matsumoto. Chaos in electronic circuits. TIIER, 1987, T.75, No.8, S.67-68, Fig. 1 and Fig. 6), containing a device with negative resistance, the first output of which connected to the first terminal of the first capacitor and the first terminal of the resistor, the second terminal of which is connected to the first terminal of the second capacitor and the first terminal of the inductor, the second terminal of which is connected to the second terminal of the second capacitor and the second terminal of the device with negative resistance.

The disadvantage of these generators is the limited ability to modify the chaotic attractor, which limits the possibility of tuning the parameters of the generated chaotic oscillations.

The closest in technical essence to the claimed device is a generator of chaotic oscillations (Prokopenko VG Generator of chaotic oscillations. Pat. 2321155. Publ. 2008, BIPM No. 9), containing the first bipolar element with inductive resistance, the first output of which is connected to the first input the output of the first nonlinear impedance converter of the first type, the second input terminal of which is connected to the first output of the second bipolar element with inductive resistance, the first output terminal of the first nonlinear azovatelya first type of impedance connected to the first terminal of the first resistor, a second output terminal of the first nonlinear transformer of the first type of impedance connected to the first terminal of the bipolar element to the capacitive impedance.

The disadvantage of this generator of chaotic oscillations is that the properties of the chaotic attractor in it are determined by the characteristics of a single nonlinear element, which limits the possibility of tuning the parameters of the generated chaotic oscillations.

The aim of the invention is to expand the limits of regulation of the parameters of a chaotic signal by expanding the possibilities of modifying the configuration of the corresponding chaotic attractor.

The purpose of the invention is achieved in that in a chaotic oscillator containing a first bipolar element with inductive resistance, the first output of which is connected to the first input terminal of the first nonlinear impedance converter of the first type, the second input terminal of which is connected to the first output of the second bipolar element with inductive resistance, the output terminal of the first non-linear impedance converter of the first type is connected to the first terminal of the first resistor, the second output terminal of the first non-linear a linear impedance converter of the first type is connected to the first terminal of the bipolar element with capacitive resistance, a second resistor is introduced, the first terminal of which is connected to the second terminal of the first resistor and the second terminal of the bipolar element with capacitive resistance, the second terminal of the second resistor is connected to the second terminal of the first bipolar element with inductive resistance, the second terminal of the second bipolar element with inductive resistance is connected to the first terminal of the first bipolar element with and inductance resistance and transfer characteristic of the first nonlinear transformer of the first type of impedance is defined by the equation

where i ₂ (i ₁ ) is the current flowing through the output terminals of the first nonlinear impedance converter of the first type, i ₁ is the current flowing through the input terminals of the first nonlinear impedance converter of the first type,

, $$g=2\left(\frac{b-a}{b-1}\right)$$

, I₀ - граничный ток между средним, проходящим через начало координат, и боковыми участками передаточной характеристики, a и b - вещественные коэффициенты, имеющие противоположные знаки, М и N - целые неотрицательные числа, напряжение на первом входном выводе первого нелинейного преобразователя импеданса первого типа равно напряжению на первом выходном выводе первого нелинейного преобразователя импеданса первого типа, напряжение на втором входном выводе первого нелинейного преобразователя импеданса первого типа равно напряжению на втором выходном выводе первого нелинейного преобразователя импеданса первого типа, первый двухполюсный элемент с индуктивным сопротивлением содержит первый линейный индуктивный элемент, первый и второй выводы которого соединены соответственно с первым и вторым выводами второго нелинейного преобразователя импеданса первого типа, третий и четвертый выводы которого являются соответственно первым и вторым выводами первого двухполюсного элемента с индуктивным сопротивлением, второй двухполюсный элемент с индуктивным сопротивлением содержит второй линейный индуктивный элемент, первый и второй выводы которого соединены соответственно с первым и вторым выводами третьего нелинейного преобразователя импеданса первого типа, третий и четвертый выводы которого являются соответственно первым и вторым выводами второго двухполюсного элемента с индуктивным сопротивлением, двухполюсный элемент с емкостным сопротивлением содержит линейный емкостной элемент, первый и второй выводы которого соединены соответственно с первым и вторым выводами нелинейного преобразователя импеданса второго типа, третий и четвертый выводы которого являются соответственно первым и вторым выводами двухполюсного элемента с емкостным сопротивлением, переменное напряжение между выводами первого двухполюсного элемента с индуктивным сопротивлением равно переменному напряжению на первом линейном индуктивном элементе, ток, протекающий в цепи первого двухполюсного элемента с индуктивным сопротивлением, равен i₁(i_L1)=I₀H₁(x), где i_L1 - переменный ток, протекающий в цепи первого линейного индуктивного элемента, $$x=\frac{i_{L1}}{I_0}$$

, $$w=\frac{i_{\mathrm{one}}}{{\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="00000066.png,00000067.png"\; state="\{\{state\}\}">I</figure-callout>}}_0}$$

, $$g=2\left(\frac{b-a}{b-\mathrm{one}}\right)$$

, I ₀ is the boundary current between the average passing through the origin and the side sections of the transfer characteristic, a and b are real coefficients with opposite signs, M and N are non-negative integers, the voltage at the first input terminal of the first nonlinear impedance converter of the first type equal to the voltage at the first output terminal of the first nonlinear impedance converter of the first type, the voltage at the second input terminal of the first nonlinear impedance converter of the first type is equal to the voltage to the second m output terminal of the first non-linear impedance converter of the first type, the first bipolar element with inductive resistance contains the first linear inductive element, the first and second conclusions of which are connected respectively to the first and second terminals of the second non-linear impedance converter of the first type, the third and fourth conclusions of which are respectively the first and the second conclusions of the first bipolar element with inductive resistance, the second bipolar element with inductive resistance um the second linear inductive element, the first and second conclusions of which are connected respectively to the first and second terminals of the third nonlinear impedance converter of the first type, the third and fourth conclusions of which are respectively the first and second terminals of the second bipolar element with inductive resistance, the bipolar element with capacitive resistance contains a linear capacitive element, the first and second conclusions of which are connected respectively to the first and second conclusions of the nonlinear impedance converter nsa of the second type, the third and fourth conclusions of which are respectively the first and second terminals of the bipolar element with capacitive resistance, the alternating voltage between the terminals of the first bipolar element with inductive resistance is equal to the alternating voltage on the first linear inductive element, the current flowing in the circuit of the first bipolar element with inductive resistance is equal to i ₁ (i _L1 ) = I ₀ H ₁ (x), where i _L1 is the alternating current flowing in the circuit of the first linear inductive element, $$x=\frac{i_{L\mathrm{one}}}{I_0}$$

,

, d₁, h₁ и s₁ - вещественные коэффициенты, причем d₁>>1, M₁ и N₁ - целые неотрицательные числа, переменное напряжение между выводами второго двухполюсного элемента с индуктивным сопротивлением равно переменному напряжению на втором линейном индуктивном элементе, ток, протекающий в цепи второго двухполюсного элемента с индуктивным сопротивлением, равен i₂(i_L2)=I₀H₂(y), где i_L2 - переменный ток, протекающий в цепи второго линейного индуктивного элемента, $$y=\frac{i_{L2}}{I_0}$$

, $$g_{\mathrm{one}}=h_{\mathrm{one}}\left(\mathrm{one}+\frac{\mathrm{one}}{d_{\mathrm{one}}}\right)$$

, d ₁ , h ₁ and s ₁ are real coefficients, with d ₁ >> 1, M ₁ and N _{1 being} non-negative integers, the alternating voltage between the terminals of the second bipolar element with inductive resistance is equal to the alternating voltage at the second linear inductive element, current flowing in the circuit of the second bipolar element with inductive resistance is i ₂ (i _L2 ) = I ₀ H ₂ (y), where i _L2 is the alternating current flowing in the circuit of the second linear inductive element, $$y=\frac{i_{L2}}{{\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="00000066.png,00000067.png"\; state="\{\{state\}\}">I</figure-callout>}}_0}$$

,

, d₂, h₂ и s₂ - вещественные коэффициенты, причем d₂>>1, M₂ и N₂ - целые неотрицательные числа, переменный ток, протекающий в цепи двухполюсного элемента с емкостным сопротивлением, равен переменному току, протекающему в цепи линейного емкостного элемента, напряжение между выводами двухполюсного элемента с емкостным сопротивлением равно u(u_c)=U₀H₃(z), где u_c - переменное напряжение на линейном емкостном элементе, U₀=I₀R, R - сопротивление резистора, $$z=\frac{u_C}{U_0}$$

, $${\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="00000057.png,00000066.png"\; state="\{\{state\}\}">g</figure-callout>}}_2=h_2\left(\mathrm{one}+\frac{\mathrm{one}}{d_2}\right)$$

, d ₂ , h ₂ and s ₂ are real coefficients, with d ₂ >> 1, M ₂ and N _{2 being} non-negative integers, the alternating current flowing in the circuit of a bipolar element with capacitive resistance is equal to the alternating current flowing in the linear circuit capacitive element, the voltage between the terminals of the bipolar element with capacitive resistance is u (u _c ) = U ₀ H ₃ (z), where u _c is the alternating voltage on the linear capacitive element, U ₀ = I ₀ R, R is the resistance of the resistor, $$z=\frac{{\mathrm{<figure-callout\; id="0"\; label="u\; C\; U"\; filenames="00000066.png,00000067.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_C}{U_{}}$$

,

, d₃, h₃ и s₃ - вещественные коэффициенты, причем d₃>>1, М₃ и N₃ - целые неотрицательные числа. $${\mathrm{<figure-callout\; id="3"\; label="g"\; filenames="00000057.png"\; state="\{\{state\}\}">g</figure-callout>}}_3=h_3\left(\mathrm{one}+\frac{\mathrm{one}}{d_3}\right)$$

, d ₃ , h ₃ and s ₃ are real coefficients, and d ₃ >> 1, M ₃ and N ₃ are non-negative integers.

In order to obtain improved accuracy and temperature stability, the first non-linear impedance converter of the first type contains a voltage amplifier, the inverting input of which is connected to the first input terminal of the first non-linear impedance converter of the first type and the first terminal of a nonlinear two-terminal device, the second terminal of which is connected to the first output of the voltage amplifier and the first terminal linear bipolar, the second output of which is connected to the first output terminal of the first nonlinear impedance converter and the first type and the non-inverting input of the voltage amplifier, the second output of which is connected to the second input and second output terminals of the first non-linear impedance converter of the first type and a common bus, the second non-linear impedance converter of the first type contains a voltage amplifier, the inverting input of which is connected to the second input of the second non-linear converter the impedance of the first type and the first output of a nonlinear bipolar, the second output of which is connected to the first output of the voltage amplifier and the first the water of the resistor, the second output of which is connected to the second output of the second non-linear impedance converter of the first type and the non-inverting input of the voltage amplifier, the second output of which is connected to the first input and first output terminals of the second non-linear impedance converter of the first type, the construction of the third non-linear impedance converter of the first type is identical to the construction the second non-linear impedance converter of the first type, the non-linear impedance converter of the second type contains efforts a voltage target, the non-inverting input of which is connected to the first input and first output terminals of a non-linear impedance converter of the second type, the second input terminal of which is connected to the first output of the voltage amplifier and the first output of the resistor, the second terminal of which is connected to the inverting input of the voltage amplifier and the first output of the non-linear two-pole, the second terminal of which is connected to the second output of the voltage amplifier and the second output terminal of a nonlinear impedance converter of the second type, each non-linear The second two-terminal network contains 1 + 2Max (Q, R) of series-connected active four-terminal networks, where Max (Q, R) is the larger of the numbers Q and R, which are equal to M and N, respectively, in the nonlinear two-terminal network included in the first nonlinear impedance converter of the first type , M ₁ and N ₁ in the non-linear two-terminal, which is part of the second non-linear impedance converter of the first type, M ₂ and N ₂ in the non-linear two-terminal, which is part of the third nonlinear impedance converter of the first type, M ₃ and N ₃ in the non-linear two-terminal, included in comp in a non-linear impedance converter of the second type, the first and second terminals of the first active four-terminal are connected respectively to the first and second terminals of the non-linear two-terminal and outputs of the corresponding first and second current generators of the non-linear two-terminal, the common buses of which are connected to the first power bus, the third and fourth conclusions of each previous active the four-terminal are connected respectively to the first and second terminals of the subsequent active four-terminal, the third and fourth conclusions of the last o, 1 + 2Max (Q, R) -th active four-terminal connected to the corresponding first and second terminals of the resistor, the linear two-terminal contains a resistor, the first and second conclusions of which are the corresponding first and second conclusions of the linear two-terminal, connected to the corresponding third and fourth the outputs of the active four-terminal, the first and second conclusions of which are connected to the outputs of the corresponding first and second current generators of the linear two-terminal, common buses of which are connected to the first power bus, each act an explicit four-terminal network contains first and second transistors whose emitters, which are the corresponding first and second terminals of the active four-terminal network, are connected to the corresponding first and second terminals of the first resistor, the collector of the first transistor is connected to the emitter of the third transistor and the base of the fourth transistor, the emitter of which is connected to the collector of the fifth transistor and the first terminal of the second resistor, the second terminal of which is connected to the base of the fifth transistor and the first terminal of the third resistor, the second terminal One of which is connected to the emitter of the fifth transistor, the base of the second transistor and the output of the first current generator, the common bus of which is connected to the first power bus and the common bus of the second current generator, the output of which is connected to the base of the first transistor, the emitter of the sixth transistor and the first output of the fourth resistor, the second the output of which is connected to the base of the sixth transistor and the first output of the fifth resistor, the second output of which is connected to the collector of the sixth transistor and the emitter of the seventh transistor, the base of which is connected inena with the collector of the second transistor and the emitter of the eighth transistor, the base and collector of which is connected to the fourth terminal of the active four-terminal and the output of the third current generator, the common bus of which is connected to the collectors of the fourth and seventh transistors, the second power bus and the common bus of the fourth current generator, the output of which is connected with the base and collector of the third transistor and the third output of the active four-terminal, each voltage amplifier contains the first and second transistors of the amplifier, the base of which x are the corresponding non-inverting and inverting inputs of the voltage amplifier, the emitter of the first amplifier transistor is connected to the collector of the third amplifier transistor and the base of the fourth amplifier transistor, the emitter of which is connected to the output of the first amplifier current generator and the emitter of the third amplifier transistor, the base of which is connected to the collector of the fourth amplifier transistor and the emitter of the second transistor of the amplifier, the collector of which is connected to the base of the fifth transistor of the amplifier and the emitter the amplifier transistor, the base and collector of which is connected to the output of the second amplifier current generator and the base of the seventh amplifier transistor, the emitter of which is connected to the collector of the first amplifier transistor, the emitter of the fifth amplifier transistor is connected to the collector of the eighth amplifier transistor and the first output of the first amplifier resistor, the second output of which connected to the base of the eighth transistor of the amplifier and the first terminal of the second resistor of the amplifier, the second terminal of which is connected to the emitter of the eighth transistor the amplifier, the output of the third amplifier current generator and the first output of the voltage amplifier, the collector of the fifth amplifier transistor is connected to the output of the fourth amplifier current generator and the emitter of the ninth amplifier transistor, the collector of which is connected to the output of the fifth amplifier current generator and the second voltage amplifier output, the base of the ninth amplifier transistor is connected with a third power bus, common buses of the first, third and fifth amplifier current generators are connected to the first power bus, common buses of the second and fourth The grounded current generators of the amplifier are connected to the collector of the seventh transistor and to the second power bus.

The inventive generator of chaotic oscillations is illustrated in figure 1, which shows its electrical circuit; figure 2, which shows the distribution of currents and voltages in the circuit of the generator during its operation; figure 3, which shows the electric circuit diagram of the first non-linear impedance converter of the first type; figure 4, which shows the electric circuit diagram of the second and third nonlinear impedance converters of the first type; 5, which shows a schematic electrical diagram of a non-linear impedance converter of the second type; 6, which shows a schematic electrical diagram of a nonlinear bipolar; Fig.7, which shows the electrical circuit diagram of the active four-port network; Fig. 8 is a circuit diagram of a circuit diagram of a voltage amplifier; Fig.9, which shows the dimensionless transfer characteristic of the first non-linear impedance converter of the first type at M = 0, N = 1; figure 10, which shows the dimensionless transfer characteristic of the second and third non-linear impedance converters of the first type and non-linear impedance converter of the second type; 11, which shows an example of the projection of a dimensionless strange attractor onto the (x, y) plane with M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0, M = 0, N = 1, a = 0.5, b = -0.35, A = 7, B = 3, D = 0.25; 12, illustrating the formation mechanism of the simplest composite multi-attractor with N ₁ = 1, M ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0, M = 0, N = 1, a = 0.5, b = -0.35, A = 7, B = 3, D = 0.25; 13, illustrating the mechanism of formation of a composite multi-attractor with M ₁ = N ₁ = 2, M ₂ = N ₂ = M ₃ = N ₃ = 0, M = 0, N = 1, a = 0.5, b = -0.35, A = 7, B = 3, D = 0.25; Fig. 14, illustrating the formation mechanism of a composite multi-attractor with M ₂ = N ₂ = 2, M ₁ = N ₁ = M ₃ = N ₃ = 0, M = 0, N = 1, a = 0.5, b = -0.35, A = 7, B = 3, D = 0.25; Fig. 15, illustrating the formation mechanism of a composite multi-attractor with M ₃ = N ₃ = 2, M ₁ = N ₁ = M ₂ = N ₂ = 0, M = 0, N = 1, a = 0.5, b = -0.35, A = 7, B = 3, D = 0.25; Fig.16, which shows a three-dimensional image of a dimensionless strange attractor at M = 0, N = 1, a = 0.5, b = -0.35, A = 7, B = 3, D = 0.25, M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 1, d ₁ = 30, d ₂ = 5, d ₃ = 100, h ₁ ≈1.61, h ₂ ≈7.775, h ₃ ≈4.67, s ₁ = 0, s ₂ ≈ 2.425, s ₃ = 0; 17, 18 and 19, which show examples of projection of this attractor on the plane (x, y), (x, z) and (y, z), respectively; FIGS. 20, 21 and 22, which show examples of time dependences of dimensionless x, y and z corresponding to the chaotic attractor in FIG. 16; Fig, which shows the distribution of currents and voltages in the circuit of the second and third nonlinear impedance converters of the first type during their operation; Fig, which shows the distribution of currents and voltages in the circuit of a nonlinear impedance converter of the second type during its operation.

The chaotic oscillator contains the first 1 and second 2 bipolar elements with inductive resistance, a bipolar element with capacitance 3, the first 4 and second 5 resistors, the first non-linear impedance converter of the first type 6, the first bipolar element with inductive resistance contains the first linear inductive element 7 and the second nonlinear impedance converter of the first type 8, the second bipolar element with inductive resistance contains a second linear inductive element 9 and a third nonlinear the first type 10 impedance converter, the capacitive bi-pole element contains a linear capacitive element 11 and the second type non-linear impedance converter 12, the first non-linear impedance converter of the first type contains a voltage amplifier 13, a linear two-terminal 14 and a non-linear two-terminal 15, the second and third non-linear impedance converters the first type contains a voltage amplifier 16, a resistor 17 and a nonlinear bipolar 18, a nonlinear impedance converter of the second type contains an amplifier a voltage 19, a resistor 20 and a non-linear two-terminal 21, a linear two-terminal contains a resistor 22, an active four-terminal 23, the first 24 and second 25 current generators of a linear two-terminal, a non-linear two-terminal contains a resistor 26, active four-terminal 27, the first 28 and second 29 current generators of a non-linear two-terminal , each active four-terminal network contains the first 30, second 31, third 32, fourth 33, fifth 34, sixth 35, seventh 36 and eighth 37 transistors, the first 38, second 39, third 40, fourth 41 and fifth 42 resistors, first 43, second 44, tre 45 and fourth 4 6 current generators, each voltage amplifier contains the first 47, second 48, third 4 9, fourth 50, fifth 51, sixth 52, seventh 53, eighth 54 and ninth 55 transistors of the amplifier, the first 56 and second 57 resistors of the amplifier The first 58, the second 59, the third 60, the fourth 61 and the fifth 62 are the current generators of the amplifier.

We write the equations describing the operation of this generator (see figure 2):

where L1 and L2 are the inductances of the first 7 and second 7 linear inductive elements; C is the capacity of the linear capacitive element 7; R1 and R2 are the resistances of the first 7 and second 7 resistors, respectively; u _L1 and u _L2 - alternating voltages on the first 3 and second 3 linear inductive elements, respectively; i _L1 and i _L2 - alternating currents flowing in the circuits of the first 6 and second 8 linear inductive elements, respectively; u _C and i _C are the alternating voltage at the linear capacitive element 0 and the alternating current flowing through it, respectively.

, $$u_{L2}=L2\frac{d{i}_{L2}}{dt}$$

, $$i_C=C\frac{d{u}_C}{dt}$$

, и разрешив уравнения (1) относительно производных $$\frac{d{i}_{L1}}{dt}$$

, $$\frac{d{i}_{L2}}{dt}$$

и $$\frac{d{u}_C}{dt}$$

, получим следующую систему дифференциальных уравнений:Given that $$u_{L\mathrm{one}}=L\mathrm{one}\frac{d{i}_{L\mathrm{one}}}{dt}$$

, $${\mathrm{<figure-callout\; id="2"\; label="u\; L"\; filenames="00000057.png,00000066.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_L=L2\frac{d{i}_{L2}}{dt}$$

, $$i_C=C\frac{d{u}_C}{dt}$$

, and solving equations (1) with respect to derivatives $$\frac{d{i}_{L\mathrm{one}}}{dt}$$

, $$\frac{d{i}_{L2}}{dt}$$

and $$\frac{d{u}_C}{dt}$$

, we obtain the following system of differential equations:

, $$y=\frac{i_{L2}}{I_0}$$

, $$z=\frac{u_C}{I_{0}R1}$$

и безразмерное время $$\tau =\frac{R1}{L2}t$$

, представим полученные уравнения в безразмерном виде:Introducing dimensionless variables $$x=\frac{i_{L\mathrm{one}}}{{\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="00000066.png,00000067.png"\; state="\{\{state\}\}">I</figure-callout>}}_0}$$

, $$y=\frac{i_{L2}}{{\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="00000066.png,00000067.png"\; state="\{\{state\}\}">I</figure-callout>}}_0}$$

, $$z=\frac{u_C}{I_{0}R\mathrm{one}}$$

and dimensionless time $$\tau =\frac{R\mathrm{one}}{L2}t$$

, we present the obtained equations in a dimensionless form:

transfer characteristic of the first nonlinear impedance converter of the first type, w = H ₂ (y) -H ₁ (x), H ₁ (x) is the dimensionless transfer characteristic of the second nonlinear impedance converter of the first type, H ₂ (y) is the dimensionless transfer characteristic of the third nonlinear an impedance converter of the first type, H ₃ (z) is the dimensionless transfer characteristic of a nonlinear impedance converter of the second type.

The image of the function H _j (w _j ), where j = 1, 2, 3, w ₁ = x, w ₂ = y, w ₃ = z, is shown in Fig. 10. It can be seen that it is a piecewise linear multi-segment function containing M _j + N _j + 1 segments with a unit slope and M _j + N _j segments with a slope -d _j . The length of the argument (x, y or z) of segments with a unit slope is 2h _j , the length of the argument of segments with a slope of -d _j is 2h _j / d _j . Coefficient S _j sets the value of the displacement of the function H _j (w _j ) relative to the origin along the unit slope passing through the coordinate origin.

This nonlinearity of the current – voltage characteristics of the reactive elements of the generator circuit is necessary in order to ensure the conditions for the formation of a composite multiattractor.

In the case of linear first 1 and second 2 capacitive and inductive 3 bipolar elements (with M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0, when H ₁ (x) = x, H ₂ (y) = y, H ₃ (z) = z) the declared generator of chaotic oscillations generates chaotic oscillations corresponding to the equations:

For example, at M = 0, N = 0, a = 0.5, b = -0.35, A = 7, B = 3, D = 0.25 M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0 , the senior characteristic Lyapunov exponent is approximately 0.1 (Fig. 11).

Now put M ₁ = 1, leaving N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0. In this case, the function H ₁ (x) will take the form shown in Fig. 12. In this case, the form of oscillations in the generator will depend on the values of the coefficients h ₁ and s ₁ that specify the position of the boundaries between the segments of the nonlinear function H ₁ (x).

As long as the boundaries do not intersect with the attractor, the oscillations in the generator do not differ from the case of the linear function H ₁ (x) = x, since the movement along the x coordinate occurs on the segment of the function H ₁ (x) with a unit slope passing through the origin. However, when h ₁ decreases to 6.7, when the maximum dimensions of the attractor along the x coordinate exceed the corresponding sizes of this segment, phase trajectories will sometimes intersect the boundary between the segments and go to the segment with the slope -d and then to the adjacent segment with a single slope.

When the operating point is found within the second linear segment with a single slope, the oscillations in the generator occur in accordance with the equations:

since the second linear segment with a unit slope is shifted relative to the first such segment along the x axis by the interval [2h ₁ -s ₁ ].

, получим систему уравненииIf we replace the variables x1 = x-2h ₁ + s ₁ and take into account that $$\frac{dx\mathrm{one}}{d\tau }=\frac{dx}{d\tau }$$

we get the system of equation

which is no different from equations (1). Therefore, when moving on an adjacent (second) segment with a unit slope, the initial chaotic attractor is reproduced, shifted relative to the original attractor by the interval [2h ₁ -s ₁ ] along the x axis.

When the trajectory crosses the boundary between the segments again, the motion will return to the initial chaotic attractor, etc. As a result, a composite chaotic attractor is formed, combining two identical attractors (Fig. 12). Similarly, a composite multi-attractor is formed with a larger number of segments in the composition of the function H ₁ (x) (Fig. 13).

In the same way, the formation of composite multiattractors, consisting of copies of the original attractor arranged along the y and z axes, is achieved by the nonlinearities of the second nonlinear impedance converter of the second type and the second nonlinear impedance converter of the first type (Fig. 14 and Fig. 15, respectively).

If two functions H _j (w _j ) are simultaneously nonlinear, the “two-dimensional” composite multiattractors are implemented in the described manner (Figs. 17, 18 and 19).

And finally, when all three functions H _j (w _j ) contain several segments with a single slope, a “three-dimensional” composite multi-attractor is formed, an example of which is shown in FIG. 16 of the description of the invention.

The values of the senior characteristic Lyapunov exponent for various values of the coefficients of equations (3) corresponding to the situations considered above are equal to:

At M = 0, N = 1, a = 0.5, b = -0.35, A = 7, B = 3, D = 0.25

- in the case of M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 0 (FIG. 12), the senior characteristic Lyapunov exponent is approximately 0.1;

- in the case of M ₁ = N ₁ = 1, M ₂ = N ₂ = M ₃ = N ₃ = 0, d ₁ = 30, h ₁ ≈1.61, s ₁ = 0 (Fig. 13), Lyapunov’s senior characteristic exponent is approximately equal 0.11;

- in the case of M ₂ = N ₂ = 1, M ₁ = N ₁ = M ₃ = N ₃ = 0, d ₂ = 5, h ₂ ≈ 7.775, s ₂ ≈-2.425 (Fig. 14), Lyapunov’s senior characteristic exponent is approximately equal to 0.1;

- in the case of M ₃ = N ₃ = 1, M ₁ = N ₁ = M ₂ = N ₂ = 0, d ₃ = 100, h ₃ ≈4.67, s ₃ = 0, the senior characteristic Lyapunov exponent is approximately 0.09;

- in the case of M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 1, d ₁ = 30, d ₂ = 5, d ₃ = 100, h ₁ ≈1.61, h ₂ ≈7.775, h ₃ ≈4.67, s ₁ = 0, s ₂ ≈-2.425, s ₃ = 0, the highest characteristic Lyapunov exponent is close to 0.11.

For given values of the coefficients a, b, A, B, D, M, N, M _j , N _j , d _j , h _j , S _j , j = 1, 2, 3, random oscillations are observed in the inventive generator, characterized by the presence of compositional strange multiattractor, consisting of several copies of the chaotic attractor shown in Fig.11.

, $$b=R5\left(\frac{1}{R3}-\frac{1}{R4}\right)$$

, $$I_0=I_1\left(1-\frac{R6}{R5}\right)$$

, где R3 - сопротивление резистора 22, входящего в состав линейного двухполюсника 14; R4 - сопротивление первого резистора 38, содержащегося в активном четырехполюснике 23, входящем в состав линейного двухполюсника 14; R5 - сопротивление первого резистора 38, содержащегося в первом активном четырехполюснике 27, входящем в состав нелинейного двухполюсника 15, содержащегося в первом нелинейном преобразователе импеданса первого типа; R6 - значение входящего в состав нелинейного двухполюсника 15 сопротивления резистора 26 и сопротивлений первых резисторов 38, содержащихся в остальных, со второго по 1+2Max(M,N)-й, активных четырехполюсниках 27, входящих в состав нелинейного двухполюсника 15, содержащегося в первом нелинейном преобразователе импеданса первого типа.The parameters of the transfer characteristic of the first nonlinear impedance converter of the first type are equal $$a=\left(\frac{\mathrm{one}}{R\mathrm{four}}-\frac{\mathrm{one}}{R3}\right)/\left(\frac{\mathrm{one}}{R6}-\frac{\mathrm{one}}{R5}\right)$$

, $$b=R5\left(\frac{\mathrm{one}}{R3}-\frac{\mathrm{one}}{R\mathrm{four}}\right)$$

, $${\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="00000066.png,00000067.png"\; state="\{\{state\}\}">I</figure-callout>}}_0=I_{\mathrm{one}}\left(\mathrm{one}-\frac{R6}{R5}\right)$$

where R3 is the resistance of the resistor 22, which is part of the linear two-terminal 14; R4 is the resistance of the first resistor 38 contained in the active four-terminal 23, which is part of the linear two-terminal 14; R5 is the resistance of the first resistor 38 contained in the first active four-terminal 27 included in the non-linear two-terminal 15 contained in the first non-linear impedance converter of the first type; R6 is the value of the resistance of the resistor 26 included in the non-linear two-terminal 15 and the resistances of the first resistors 38 contained in the second, 1 + 2Max (M, N) -th, active four-terminal 27 included in the non-linear two-terminal 15 contained in the first non-linear impedance converter of the first type.

At M = N, the current I ₁ is equal to the value of the output currents of the third 45 and fourth 46 current generators, which are part of the active four-terminal 27 contained in the nonlinear two-terminal 15, which is part of the first nonlinear impedance converter of the first type. The value of the output currents I _{2 of} the current generators 28 and 29 contained in the nonlinear two-terminal network 15, which is part of the first nonlinear impedance converter of the first type, is determined by the expression I ₂ = KI ₁ , where K = 1 + 2Max (M, N) is the number active four-terminal 27 as part of a non-linear two-terminal 15, which is part of the first non-linear impedance converter of the first type.

The value of the output currents I _{3 of the} third 45 and the fourth 46 current generators included in the active four-terminal 23 contained in the linear two-terminal 14 is equal to the value of the output currents I _{4 of the} current generators 24 and 25 contained therein, I ₃ = I ₄ .

Moreover, the values of currents I ₃ and I _{4 are} determined by the expression I ₃ = I ₄ ≥2I ₂ .

The case M> N differs from the case M = N in that the output currents of the third current generators 45 included in the 2 (MN) -th and 2 (MN) -1-st active four-terminal 27 contained in the nonlinear two-terminal 15 included in the composition of the first nonlinear impedance converter of the first type, respectively, increase and decrease by the same amount ΔI = (0.7 ... 0.9) I ₁ .

The case N> M differs from the case M = N in that the output current of the fourth current generators 46 included in the 2 (NM) and 2 (NM) of the 1st active four-terminal 27 contained in the nonlinear two-terminal 15 included in the composition of the first nonlinear impedance converter of the first type, respectively, increase and decrease by the same amount equal to (0.7 ... 0.99) I ₁ .

The parameters of the transfer characteristic of the nonlinear impedance converter of the second type are equal

the resistance of the resistor 20 included in the non-linear impedance converter of the second type;

R11 is the resistance of the first resistor 38 contained in the first active four-terminal 27 included in the nonlinear two-terminal 21 contained in the non-linear impedance converter of the second type; R12 is the resistance value of the resistor 2 6, which is part of the nonlinear bipolar 21, and the resistances of the first resistors 38, contained in the remaining, from the second to 1 + 2Max (M ₃ , N ₃ ) -th, active four-terminal 27, which are part of the nonlinear bipolar 21 contained in a non-linear impedance converter of the second type.

With M ₃ = N _{3, the} currents I ₁₃ and J ₁₃ are equal to the values of the output currents of the third 45 and fourth 46 current generators, which are part of the odd, with the exception of the first, active four-terminal 27, and the values of the output currents of the fourth 46 and third 45 current generators, respectively included in the composition of the even active four-terminal 27 contained in the non-linear two-terminal 21, which is part of a non-linear impedance converter of the second type. In this case, the value of the output currents I _{23 of} the current generators 28 and 29 contained in the nonlinear bipolar 21, which is part of the nonlinear impedance converter of the second type, is determined by the expression I ₂₃ = K ₃ (I ₁₃ + J ₁₃ ) + I ₃₃ , where K ₃ = Max (M ₃ , N ₃ ), I ₃₃ - the value of the output currents of the third 45 and fourth 46 current generators that are part of the first active four-terminal 27 contained in the nonlinear two-terminal 21, which is part of the non-linear impedance converter of the second type, and the current I ₃₃ several times more current Max (I _13, J _13), where Max (I _13, J ₁₃₎ - of cities account for major currents I ₁₃ and J _13, i.e.

I ₃₃ = (2 ... 5) Max (I ₁₃ , J ₁₃ ).

The case of M ₃ <N ₃ differs from the case of M ₃ = N ₃ in that the output current of the third 45 current generator, which is part of the 1 + 2 (N ₃ -M ₃ ) active four-terminal 27, contained in the nonlinear two-terminal 21, included the non-linear impedance converter of the second type is set equal to the current I ₃₃ , and the output current of the third 45 current generator, which is part of the first active four-terminal 27 contained in the non-linear two-terminal 21, which is part of the non-linear impedance converter of the second type, is set to the current I ₁₃ .

The case of N ₃ <M ₃ differs from the case of M ₃ = M ₃ in that the output current of the fourth 46 current generator, which is part of the 1 + 2 (M ₃ -N ₃ ) active four-terminal 27, contained in the nonlinear two-terminal 21, included the composition of the nonlinear impedance converter of the second type is equal to the current I ₃₃ , and the output current of the fourth 46 current generator, which is part of the first active four-terminal 27 contained in the nonlinear two-terminal 21, which is part of the nonlinear impedance converter of the second type, is set to current J ₁₃ .

, $$h_j+s_j=\frac{I_0{}_j}{I_0}$$

, $$h_j+s_j=\frac{J_0{}_j}{I_0}$$

, $$I_0{}_j=\frac{I_1{}_j}{1+\frac{1}{dj}}$$

, $$J_0{}_j=\frac{J_1{}_j}{1+\frac{1}{dj}}$$

, при том, что $$\frac{R{7}_j}{R{9}_j}=1+\frac{1}{d_j}$$

, где j=1 в случае второго и j=2 в случае третьего нелинейных преобразователей импеданса первого типа, R7_j - сопротивление резистора 17, входящего в состав второго или третьего нелинейного преобразователя импеданса первого типа; R8_j - сопротивление первого резистора 38, содержащегося в первом активном четырехполюснике 27, входящем в состав нелинейного двухполюсника 18, содержащегося во втором или третьем нелинейном преобразователе импеданса первого типа; R9_j - значение входящего в состав нелинейного двухполюсника 18 сопротивления резистора 26 и сопротивлений первых резисторов 38, содержащихся в остальных, со второго по 1+2Мах(M_j, N_j)-й, активных четырехполюсниках, входящих в состав нелинейного двухполюсника 18, содержащегося во втором или третьем нелинейном преобразователе импеданса первого типа.The parameters of the transfer characteristic of the second and third nonlinear impedance converters of the first type are equal $$d_j=\frac{R{8}_j}{R{7}_j}$$

, $$h_j+s_j=\frac{I_0{}_j}{I_0}$$

, $$h_j+s_j=\frac{J_0{}_j}{I_0}$$

, $$I_0{}_j=\frac{I_{\mathrm{one}}{}_j}{\mathrm{one}+\frac{\mathrm{one}}{dj}}$$

, $$J_0{}_j=\frac{J_{\mathrm{one}}{}_j}{\mathrm{one}+\frac{\mathrm{one}}{dj}}$$

, despite the fact that $$\frac{R{7}_j}{R{9}_j}=\mathrm{one}+\frac{\mathrm{one}}{d_j}$$

where j = 1 in the case of the second and j = 2 in the case of the third nonlinear impedance transducers of the first type, R7 _j is the resistance of the resistor 17, which is part of the second or third nonlinear impedance transducer of the first type; R8 _j is the resistance of the first resistor 38 contained in the first active four-terminal 27, which is part of the nonlinear two-terminal 18, contained in the second or third nonlinear impedance converter of the first type; R9 _j is the value of the resistance of the resistor 26 that is part of the nonlinear bipolar 18 and the resistances of the first resistors 38 contained in the second, 1 + 2Max (M _j , N _j ) -th, active four-terminal circuits that are part of the non-linear two-terminal 18 contained in a second or third non-linear impedance converter of the first type.

With M _j = N _{j, the} currents I _1j and J _1j are equal to the values of the output currents of the fourth 46 and third 45 current generators, which are part of the odd, with the exception of the first, active four-terminal 27, and the values of the output currents of the third 45 and fourth 46 current generators, respectively included in the composition of even active four-terminal 27 contained in the non-linear two-terminal 18, which is part of the second or third non-linear impedance converter of the first type. The value of the output currents I _{2j of} the current generators 28 and 29 contained in the nonlinear two-terminal network 18, which is part of the second or third nonlinear impedance converter of the first type, is determined by the expression I _2j = K _j (I _1j + J _1j ) + I _3j , where K _j = Max (M _j , N _j ), I _3j is the value of the output currents of the third 45 and fourth 46 current generators, which are part of the first active four-terminal 27, contained in non-linear two-terminal 18, which is part of the second or third non-linear impedance converter of the first type, and the current I _3j in several p much greater than the current Max (I _1j , J _1j ), where Max (I _1j , J _1j ) is the largest of the currents I _1j and J _1j , that is, I _3j = (2 ... 5) Max (I _1j , J _1j ).

The case M _j <N _j differs from the case M _j = N _j in that the output current of the third 45 current generator, which is part of the 1 + 2 (N _j -M _j ) active four-terminal network 27, contained in the nonlinear two-terminal network 18, included the composition of the second or third nonlinear impedance converter of the first type is set equal to the current I _3j , and the output current of the third 45 of the current generator included in the first active four-terminal 27 contained in the nonlinear two-terminal 18, which is part of the second or third nonlinear impedance converter of the first type, is set equal to the current J _1j .

The case N _j <M _j differs from the case M _j = N _j in that the output current of the fourth 46 current generator included in the 1 + 2 (M _j -N _j ) active four-terminal 27 contained in the non-linear two-terminal 18 included the second non-linear impedance converter of the first type is equal to the current I _3j , and the output current of the fourth 46 current generator included in the first active four-terminal 27 contained in the non-linear two-terminal 18, which is part of the second or third non-linear impedance converter of the first type, is set equal to the current I _1j .

The resistances of the second 39, third 40, fourth 41 and fifth 42 resistors and the output currents of the first 43 and second 44 current generators contained in each active four-terminal network are connected by the following relations I ₅ R14 = (1.2 ... 2) U _be , R13 = (1 ... 10) R14, where R13 is the value of the resistances of the second 39 and fifth of 42 resistors, R14 is the value of the resistances of the third 40 and fourth of 41 resistors, I ₅ is the value of the output currents of the first 43 and second 44 current generators, U _be is the value of the base-emitter dressing of the fifth 34 and the sixth 35 transistors that make up the active four-pole yusnika.

The output currents of the current generators contained in the voltage amplifier must satisfy the following relations I _yl = 2I _y2 , I _y3 + I _y5 = I _y4 , where I _y1 is the output current of the first 58 current generator of the amplifier, I _y2 is the output current of the second 59 current generator amplifier, I _y3 is the output current of the third 60 current generator of the amplifier, I _y4 is the output current of the fourth 61 current generator of the amplifier, I _y5 is the output current of the fifth 62 current generator of the amplifier. Moreover, the values of the currents I _y3 and I _y5 should be several times higher than the values of the output currents of the first 28 and second 29 current generators contained in the nonlinear two-terminal network, which is part of the nonlinear impedance converter together with this voltage amplifier.

The resistances of the first 56 and second 57 resistors of the amplifier and the output current of the third 60 current generator contained in the voltage amplifier are related by the following relations I _y3 R15 = (1.2 ... 2) U _be , R15 = (1 ... 15) R16, where R15 and R16 are the values of the resistances of the first 56 and second 57 resistors of the amplifier, U _be - the value of the base-emitter circuit of the eighth 54 transistor of the amplifier.

The second and third non-linear impedance converters of the first type are impedance converters that change the impedance by converting current (I-PI), which operate as follows (Fig.23). Each of them contains a differential voltage amplifier with a high gain having an additional current output. The amplifier has high input impedances at both inputs and a low output impedance at the first output. An additional (second) output is the output of a current repeater with a high output resistance. Its purpose is to generate a current equal to the current flowing through the first low-resistance amplifier output, so that the alternating current flowing into the first amplifier output is equal to the alternating current flowing from the second amplifier output (Fig. 23).

Given that the potential difference between the inputs of the voltage amplifier and its input currents is negligible, the voltage between the outputs of the non-linear impedance converter is equal to the voltage on the linear inductive element (for example, the inductor), in addition, the voltages on the linear and non-linear resistors are equal. A current equal to the current in the circuit of the linear inductive element flows through the non-linear resistor. As a result, a voltage drop u _НЛ (i _L ) depending on the current in the linear inductive element arises, under the action of which a current i (i _L ) = u _НЛ (i _L ) / R flows in the linear resistor circuit. At the same time, the current i _L -i (i _L ) enters the first, low-impedance output of the amplifier, the same current flows from the second output of the amplifier and, together with the current 4, enters an external circuit. That is, the current flowing in the circuit of the linear resistor i (i _L ) enters the external circuit.

Thus, when a linear inductive element is connected to an external circuit through a second or third non-linear impedance converter of the first type, a current i (i _L ) flows through the outputs of the converter, and a voltage u _L drops between them. That is, the combination of linear inductance and the second (or third) nonlinear impedance converter of the first type forms an equivalent nonlinear inductive element with the required current-voltage characteristic.

The non-linear impedance converter of the second type (Fig.24) is an impedance converter that changes the impedance by voltage conversion (U-PI), which operates as follows. It contains the same amplifier as the second and third non-linear impedance converters of the first type. Since the potential difference between the inputs of the amplifier is negligible, the voltage drop across the resistor R is equal to the voltage drop across the linear capacitive element (capacitor), therefore, the current i ₁ flowing in this resistor is equal to u _C / R; the same current flows in the circuit of the nonlinear resistor R _NL , the voltage on which depends on the current i ₁ flowing through it, and therefore, on the capacitor voltage u _NL (i ₁ ) = u _NL (u _C / R).

Due to the negligible potential difference between the inputs of the amplifier, the voltage between the first and second outputs of the non-linear impedance converter of the second type is equal to the voltage drop across the non-linear resistor u _NL (u _C / R). In this case, the current flowing through the capacitor is equal to the sum of the current i ₁ flowing in the circuit of the resistors R and R _NL and the current i _C -i ₁ flowing in the circuit of the first and second outputs of the amplifier. Therefore, a current equal to the current flowing through the linear capacitive element flows through the output of the non-linear impedance converter of the second type (Fig. 23).

Thus, when a linear capacitive element is connected to an external circuit through a non-linear impedance converter of the second type, a current equal to the current flowing in the linear capacitive element flows through the converter outputs, and the voltage drop between the converter outputs is u _NL (u _C / R) = u ₁ (u _C ). That is, the combination of a capacitor and a non-linear impedance converter of the second type forms an equivalent non-linear capacitive element with a given current-voltage characteristic.

An example of a practical implementation of the claimed generator of chaotic oscillations is a circuit having the following parameters.

Let R1 = 400 Ohm, L1 = 10 mH, R3 = 600 Ohm, R5 = 150 Ohm, R7 ₁ = 1033 Ohm, R7 ₂ = 1200 Ohm, R10 = 1010 Ohm, I ₀ = 400 μA. Then, in the case of M ₁ = N ₁ = M ₂ = N ₂ = M ₃ = N ₃ = 1, d ₁ = 30, d ₂ = 5, d ₃ = 100, h ₁ ≈1.61, h ₂ ≈7.775, h ₃ ≈4.67, s ₁ = 0, s ₂ ≈-2.425, s ₃ = 0, for M = 0, N = 1, a = 0.5, b = -0.35, A = 7, B = 3, D = 0.25, chaotic oscillations corresponding to these parameters of equations (3) are observed at the following values of the oscillatory system of the generator: С≈0.145 μF, L1≈70 mH, R2 = 100 Ohms, the first nonlinear impedance converter of the first type: R4≈250 Ohms, R6≈110 Ohms, I ₁ ≈1.5 mA, I ₂ ≈4.5 mA, I ₃ = I ₄ ≈5 mA, the second non-linear impedance converter of the first type: R8 ₁ ≈32 kOhm, R9 ₁ ≈1 kOhm, I ₁₁ = J ₁₁ ≈0.67 mA, I ≈6.34 ₂₁ mA, I ≈5 ₃₁ mA, and the third nonlinear transformer pedansa first type: R8 ≈5.3 ₂ kilohms, R9 ≈1 ₂ kohm, I ≈2.6 ₁₂ mA, J ≈4.9 ₁₂ mA, I ≈27.5 ₂₂ mA, I ₃₂ ≈20 mA nonlinear transformer of the impedance of the second type: R11≈105 kohm , R12≈1 kOhm, I ₁₃ ≈J ₁₃ ≈0.75 mA, I ₂₃ ≈5.5 mA, I ₃₃ ≈4 mA, voltage amplifier: R15≈10 kOhm, R16≈1 kOhm, I _y1 ≈400 μA, I _y2 ≈200 μA, I _y3 = I _y5 ≈10 mA, I _y4 ≈20 mA, elements of DC bias circuits in nonlinear impedance converters: R13≈5 kOhm, R14≈1 kOhm, I5≈2 mA.

Examples of the dimensionless strange attractor corresponding to these values of the generator parameters, its projections on the (x, y), (x, z) and (y, z) planes, as well as examples of the time-dependent dimensionless variables x, y and z, are shown in FIG. 16-22.

The increased accuracy and temperature stability of non-linear impedance converters is due to the fact that their transfer characteristics are practically independent of the parameters of the transistors, due to the mutual compensation of the emitter resistances of the transistors 29 and 31, as well as 30 and 36 as part of active four-terminal devices, and also due to an increase in the gain and minimization DC voltage differences on the inverting and non-inverting inputs of the voltage amplifier due to the introduction of transistors 46, 47 and 50, 51.

Thus, the claimed generator of chaotic oscillations compares favorably with the prototype and analogues, in which the chaotic signal can be tuned only by changing the parameters of the original chaotic attractor, in that it allows you to implement a composite chaotic multiattractor obtained by combining the original chaotic attractor with one or more copies of it as a result of which its restructuring can be additionally carried out by changing the number and relative position of its constituent components, Thanks to what stated generator has a much greater capacity adjustment parameters of the generated chaotic signal.

Claims (2)

1. A chaotic oscillation generator containing a first bipolar element with inductive resistance, a first output of which is connected to a first input terminal of a first non-linear impedance converter of the first type, a second input terminal of which is connected to a first output of a second bipolar element with inductive resistance, a first output terminal of a first non-linear converter the impedance of the first type is connected to the first terminal of the first resistor, the second output terminal of the first nonlinear impedance converter ne of the first type is connected to the first terminal of the bipolar element with capacitive resistance, characterized in that a second resistor is inserted into it, the first terminal of which is connected to the second terminal of the first resistor and the second terminal of the bipolar element with capacitive resistance, the second terminal of the second resistor is connected to the second terminal of the first bipolar element with inductive resistance, the second terminal of the second bipolar element with inductive resistance is connected to the first terminal of the first bipolar element with inductive resistance, wherein the transfer characteristic of the first nonlinear transformer of the first type of impedance is defined by the equation

,
where i ₂ (i ₁ ) is the current flowing through the output terminals of the first nonlinear impedance converter of the first type, i ₁ is the current flowing through the input terminals of the first nonlinear impedance converter of the first type,

,

, I ₀ is the boundary current between the average passing through the origin and the side sections of the transfer characteristic, and b are real coefficients with opposite signs, M and N are non-negative integers, the voltage at the first input terminal of the first nonlinear impedance converter of the first type equal to the voltage at the first output terminal of the first non-linear impedance converter of the first type, the voltage at the second input terminal of the first non-linear impedance converter of the first type is equal to the voltage to second m output terminal of the first non-linear impedance converter of the first type, the first bipolar element with inductive resistance contains the first linear inductive element, the first and second conclusions of which are connected respectively to the first and second terminals of the second non-linear impedance converter of the first type, the third and fourth conclusions of which are respectively the first and the second conclusions of the first bipolar element with inductive resistance, the second bipolar element with inductive resistance there is a second linear inductive element, the first and second conclusions of which are connected respectively to the first and second terminals of the third non-linear impedance converter of the first type, the third and fourth conclusions of which are respectively the first and second outputs of the second bipolar element with inductive resistance, the bipolar element with capacitive resistance contains a linear capacitive element, the first and second conclusions of which are connected respectively to the first and second conclusions of the nonlinear impedance converter nsa of the second type, the third and fourth conclusions of which are respectively the first and second terminals of the bipolar element with capacitive resistance, the alternating voltage between the terminals of the first bipolar element with inductive resistance is equal to the alternating voltage on the first linear inductive element, the current flowing in the circuit of the first bipolar element with inductive resistance is equal to i ₁ (i _L1 ) = I ₀ H ₁ (x), where i _L1 is the alternating current flowing in the circuit of the first linear inductive element,

,

, d ₁ , h ₁ and s ₁ are real coefficients, with d ₁ >> 1, M ₁ and N _{1 being} non-negative integers, the alternating voltage between the terminals of the second bipolar element with inductive resistance is equal to the alternating voltage at the second linear inductive element, current flowing in the circuit of the second bipolar element with inductive resistance is i ₂ (i _L2 ) = I ₀ H ₂ (y), where i _L2 is the alternating current flowing in the circuit of the second linear inductive element,

,

, d ₂ , h ₂ and s ₂ are real coefficients, and d ₂ >> 1, M ₂ and N ₂ are non-negative integers, the alternating current flowing in the circuit of a bipolar element with capacitive resistance is equal to the alternating current flowing in the linear circuit capacitive element, the voltage between the terminals of the bipolar element with capacitive resistance is u (u _C ) = u ₀ H ₃ (z), where u _C is the alternating voltage on the linear capacitive element, U ₀ = I ₀ R, R is the resistance of the resistor,

,

, d ₃ , h ₃ and s ₃ are real coefficients, and d ₃ >> 1, M ₃ and N ₃ are non-negative integers. 2. The chaotic oscillation generator according to claim 1, characterized in that the non-linear impedance converter of the first type contains a voltage amplifier, the inverting input of which is connected to the first input terminal of the first non-linear impedance converter of the first type and the first terminal of the nonlinear two-terminal, the second terminal of which is connected to the first output a voltage amplifier and a first terminal of a linear two-terminal device, the second terminal of which is connected to a first output terminal of a first non-linear impedance converter of the first type and a non-inverting input of a voltage amplifier, the second output of which is connected to the second input and second output terminals of the first non-linear impedance converter of the first type and a common bus, the second non-linear impedance converter of the first type contains a voltage amplifier, the inverting input of which is connected to the second input of the second non-linear impedance converter of the first type and the first output of a nonlinear bipolar, the second output of which is connected to the first output of the voltage amplifier and the first output of the resistor RA, the second output of which is connected to the second output of the second non-linear impedance converter of the first type and the non-inverting input of the voltage amplifier, the second output of which is connected to the first input and first output terminals of the second non-linear impedance converter of the first type, the construction of the third non-linear impedance converter of the first type is identical to the construction of the second a non-linear impedance converter of the first type, a non-linear impedance converter of the second type contains an amplifier a non-inverting input of which is connected to the first input and first output terminals of a non-linear impedance converter of the second type, the second input terminal of which is connected to the first output of the voltage amplifier and the first output of the resistor, the second output of which is connected to the inverting input of the voltage amplifier and the first output of the non-linear two-pole, second the output of which is connected to the second output of the voltage amplifier and the second output terminal of a non-linear impedance converter of the second type, each non-linear two-field yusnik contains 1 + 2Max (Q, R) of series-connected active four-terminal, where Max (Q, R) is the larger of the numbers Q and R, which are equal to M and N respectively in the nonlinear two-terminal, which is part of the first nonlinear impedance converter of the first type, M ₁ and N ₁ in the non-linear two-terminal, which is part of the second non-linear impedance converter of the first type, M ₂ and N ₂ in the non-linear two-terminal, which is part of the third nonlinear impedance converter of the first type, M ₃ and N ₃ in the non-linear two-terminal, which is part nonlinear of the impedance converter of the second type, the first and second terminals of the first active four-terminal are connected respectively to the first and second terminals of the non-linear two-terminal and outputs of the corresponding first and second current generators of the non-linear two-terminal, the common buses of which are connected to the first power bus, the third and fourth conclusions of each previous active four-terminal connected respectively to the first and second terminals of the subsequent active four-terminal network, the third and fourth terminals of the latter, 1 + 2Max (Q, R) -g , the active four-terminal are connected to the corresponding first and second terminals of the resistor, the linear two-terminal contains a resistor, the first and second conclusions of which are the corresponding first and second conclusions of the linear two-terminal, connected to the corresponding third and fourth terminals of the active four-terminal, the first and second conclusions of which are connected to the outputs the respective first and second current generators of the linear two-terminal network, the common buses of which are connected to the first power bus, each active four The output terminal contains first and second transistors, the emitters of which are the corresponding first and second terminals of the active four-terminal, connected to the corresponding first and second terminals of the first resistor, the collector of the first transistor is connected to the emitter of the third transistor and the base of the fourth transistor, the emitter of which is connected to the collector of the fifth transistor and the first terminal of the second resistor, the second terminal of which is connected to the base of the fifth transistor and the first terminal of the third resistor, the second terminal of which connected to the emitter of the fifth transistor, the base of the second transistor and the output of the first current generator, the common bus of which is connected to the first power bus and the common bus of the second current generator, the output of which is connected to the base of the first transistor, the emitter of the sixth transistor and the first output of the fourth resistor, the second output of which connected to the base of the sixth transistor and the first terminal of the fifth resistor, the second terminal of which is connected to the collector of the sixth transistor and the emitter of the seventh transistor, the base of which is connected to the the lecturer of the second transistor and the emitter of the eighth transistor, the base and collector of which are connected to the fourth terminal of the active four-terminal network and the output of the third current generator, the common bus of which is connected to the collectors of the fourth and seventh transistors, the second power bus and the common bus of the fourth current generator, the output of which is connected to the base and the collector of the third transistor and the third output of the active four-terminal, each voltage amplifier contains the first and second transistors of the amplifier, the bases of which are the corresponding non-inverting and inverting inputs of the voltage amplifier, the emitter of the first amplifier transistor is connected to the collector of the third amplifier transistor and the base of the fourth amplifier transistor, the emitter of which is connected to the output of the first amplifier current generator and the emitter of the third amplifier transistor, the base of which is connected to the collector of the fourth amplifier transistor and the emitter of the second an amplifier transistor whose collector is connected to a base of a fifth amplifier transistor and an emitter of a sixth trans the amplifier stator, the base and collector of which is connected to the output of the second amplifier current generator and the base of the seventh amplifier transistor, the emitter of which is connected to the collector of the first amplifier transistor, the emitter of the fifth amplifier transistor is connected to the collector of the eighth amplifier transistor and the first output of the first amplifier resistor, the second output of which is connected with the base of the eighth transistor of the amplifier and the first terminal of the second resistor of the amplifier, the second terminal of which is connected to the emitter of the eighth transistor of the amplifier, the output of the third amplifier current generator and the first output of the voltage amplifier, the collector of the fifth amplifier transistor is connected to the output of the fourth amplifier current generator and the emitter of the ninth amplifier transistor, the collector of which is connected to the output of the fifth amplifier current generator and the second voltage amplifier output, the base of the ninth amplifier transistor is connected to the third power bus, common buses of the first, third and fifth amplifier current generators are connected to the first power bus, common buses of the second and fourth gene tors current amplifier connected to the collector of the seventh transistor and a second power supply bus.

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