RU2207708C2 - Hyperchaotic wave oscillator - Google Patents

Abstract

FIELD: radio engineering; hyperchaotic electromagnetic wave sources. SUBSTANCE: oscillator has linear and negative-resistance nonlinear devices, two capacitors, and two inductance coils; effective section of current-voltage characteristic of negative- resistance nonlinear device is found from given mathematical expression. EFFECT: enlarged control capabilities of hyperchaotic signal parameters. 2 cl, 8 dwg

Description

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

 A known generator of hyperchaotic oscillations (P. Arena, S. Baglio, L. Fortuna and G. Manganaro. Hyperchaos from cellular neural networks. // Electronics Letters, 1995, vol. 31, No. 4, p. 250, Fig. 1), comprising a linear and non-linear device with negative resistance, the first terminals of which are connected to each other and with the first terminals of the first and second capacitors, the second terminal of the linear negative resistance is connected to the second terminal of the first capacitance and the first terminal of the first inductance, the second terminal of which is connected to the second terminal of the second capacitor and with the first output of the second inductance, second the first output of which is connected to the second output of a non-linear device with negative resistance.

 The disadvantage of this generator is the insignificant ability to control the parameters of the generated oscillations.

 Closest to the technical nature of the claimed device is a generator of hyperchaotic oscillations (T. Matsumoto, LO Chua and K. Kobayashi. Hyperchaos: Laboratory Experiment and Numerical Confirmation. // IEEE Transactions on Circuits and Systems, 1986, vol. CAS-33, N11 , p.1144) containing a linear and non-linear device with negative resistance, the first terminals of which are connected to the first terminal of the first capacitor, the second terminal of which is connected to the first terminal of the first inductor, the second terminal of which is connected to the second terminal of the non-linear device with negative resistance iem and the first terminal of the second capacitor, a second terminal coupled to a first terminal of the second inductor.

 The disadvantage of this generator of hyperchaotic oscillations is the limited ability to change the parameters of the generated signal.

 The purpose of the invention is the expansion of the ability to control the parameters of the hyperchaotic signal.

где u - напряжение, возникающее между выводами нелинейного устройства с отрицательным сопротивлением под действием протекающего через них тока i, R - абсолютное значение эквивалентного отрицательного сопротивления линейного устройства с отрицательным сопротивлением, I₀ - граничный ток между средним и сопредельными с ним боковыми участками вольт-амперной характеристики нелинейного устройства с отрицательным сопротивлением, λ и k - константы, удовлетворяющие соотношениям λ<0, λk>1,

М и N - целые неотрицательные числа.The purpose of the invention is achieved in that the generator of hyperchaotic oscillations, containing a linear and non-linear device with negative resistance, the first terminals of which are connected to the first terminal of the first capacitor, the second terminal of which is connected to the first terminal of the first inductor, the second terminal of which is connected to the second terminal of the non-linear device with negative resistance and the first terminal of the second capacitor, the second terminal of which is connected to the first terminal of the second inductor, is Thus, the second output of the linear device with negative resistance is connected to the second output of the first capacitor, and the second output of the second inductor is connected to the first output of the first capacitor, and the working section of the current-voltage characteristic of the nonlinear device with negative resistance is determined by the equation

where u is the voltage arising between the terminals of a nonlinear device with negative resistance under the influence of current i flowing through them, R is the absolute value of the equivalent negative resistance of a linear device with negative resistance, I ₀ is the boundary current between the middle and adjacent side sections of the current-voltage characteristics of a nonlinear device with negative resistance, λ and k are constants satisfying the relations λ <0, λk> 1,

M and N are non-negative integers.

 In order to enable electronic regulation and increase the temperature stability of the generated signal parameters, the negative-resistance linear device contains a first impedance converter, the first and second input terminals of which are the first and second negative-resistance linear device outputs, the first and second load terminals of the first impedance converter are connected with the first conclusions of the corresponding first and second resistors, the second conclusions of which are connected With a common bus, a non-linear device with negative resistance contains 3 + 2Max (M, N) series-connected four-terminal devices, where Max (M, N) is the largest of the numbers M and N, the first and second conclusions of the first four-terminal device are connected through the corresponding third and fourth resistors, respectively, with the first and second terminals of a non-linear device with negative resistance and outputs of the corresponding first and second current generators, the common buses of which are connected to the first power bus, the third and fourth conclusions of each previous the repole are connected respectively to the first and second terminals of the subsequent four-terminal, each four-terminal contains an impedance converter, the first and second input terminals of which are the corresponding first and second terminals of the four-terminal, the first and second load terminals of the impedance converter, which are the corresponding third and fourth conclusions of the four-terminal, are connected to the corresponding the first and second terminals of the resistor and the outputs of the corresponding first and second current generators a, the common buses of which are connected to the second power bus, each impedance converter contains first and second transistors, the emitters of which are the corresponding first and second input terminals of the impedance converter, the collector of the first transistor is connected to the emitter of the third transistor, the collector of which is the first load terminal of the impedance converter connected to the base and collector of the fourth transistor, the emitter of which is connected to the base of the third transistor and the collector of the fifth transistor, the base of which is connected the collector of the second transistor and the emitter of the sixth transistor, whose collector, which is the second load terminal of the impedance converter, is connected to the base and collector of the seventh transistor, the emitter of which is connected to the base of the sixth transistor and the collector of the eighth transistor, the base of which is connected to the collector of the first transistor and the second transistors are connected to the emitters of the corresponding fifth and eighth transistors and the outputs of the corresponding first and second current generators of the converter and pedansa common bus are connected to the first power bus.

 The inventive generator of hyperchaotic oscillations is illustrated in figure 1, which shows its electrical circuit diagram, figure 2, which shows the electrical circuit of the impedance converter, which is part of the generator of hyperchaotic oscillations, figure 3, which shows the distribution of currents and voltages in the generator circuit during his work, figure 4, which shows the normalized current-voltage characteristic of a nonlinear device with negative resistance at M = N = 2, figure 5 and figure 6, which depict examples of projection without azmernogo strange attractor in the plane (z, w), corresponding to the cases of M = 0, N = 1 (Figure 5) and M = N = 2 (Figure 6) as well as 7 and FIG. 8, which shows examples of the dependence of the dimensionless variable w on time, corresponding to the cases M = 0, N = 1 (Fig. 7) and M = N = 2 (Fig. 8).

 The hyperchaotic oscillator contains linear 1 and nonlinear 2 devices with negative resistance, the first 3 and second 4 capacitors, the first 5 and second 6 inductors, and the linear device with negative resistance contains the first impedance converter 7 and the first 8 and second 9 resistors, a nonlinear device with negative resistance contains the third 10 and fourth 11 resistors, the first 12 and second 13 current generators and series-connected four-terminal 14, each of which contains an impedance converter Ansa 15, first 16 and second 17 current generators and resistor 18, each impedance converter contains the first 19, second 20, third 21, fourth 22, fifth 23, sixth 24, seventh 25 and eighth 26 transistors, first 27 and second 28 current generators impedance converter.

где u(i) - вольт-амперная характеристика нелинейного устройства с отрицательным сопротивлением 2; С1 и С2 - емкости первого 3 и второго 4 конденсаторов соответственно; L1 и L2 - индуктивности первой 5 и второй 6 катушек индуктивности соответственно; i_R, i, i_L1, i_L2, i_C1 - переменные токи, протекающие соответственно в линейном 1 и нелинейном 2 устройствах с отрицательным сопротивлением, первой 5 и второй 6 катушках индуктивности и первом конденсаторе 3; u_C1, u_C2, u_L1, u_L2 - переменные напряжения на первом 3 и втором 4 конденсаторах и первой 5 и второй 6 катушках индуктивности соответственно.To find the conditions for the generation of hyperchaotic oscillations in the inventive generator, we write the equations describing its dynamics (see figure 3):

where u (i) is the current-voltage characteristic of a nonlinear device with negative resistance 2; C1 and C2 - capacitance of the first 3 and second 4 capacitors, respectively; L1 and L2 are the inductances of the first 5 and second 6 inductors, respectively; i _R , i, i _L1 , i _L2 , i _C1 - alternating currents flowing in linear 1 and nonlinear 2 devices with negative resistance, the first 5 and second 6 inductors and the first capacitor 3, respectively; u _C1 , u _C2 , u _L1 , u _L2 - alternating voltages on the first 3 and second 4 capacitors and the first 5 and second 6 inductors, respectively.

и

получим следующую систему дифференциальных уравнений:

Вводя безразмерные переменные

и безразмерное время

приведем систему (2) к безразмерному виду:

- безразмерная вольт-амперная характеристика нелинейного устройства с отрицательным сопротивлением.By solving equations (1) with respect to

and

we get the following system of differential equations:

Introducing dimensionless variables

and dimensionless time

we bring the system (2) to a dimensionless form:

- dimensionless current-voltage characteristic of a nonlinear device with negative resistance.

где R_np - абсолютное значение эквивалентного отрицательного сопротивления линейного устройства с отрицательным сопротивлением в прототипе; С1_nр и С2_nр - емкости соответственно первого и второго конденсаторов в прототипе; L1_nр и L2_np - индуктивности соответственно второй и первой катушек индуктивности в прототипе; i_L1np, i_L2np - переменные токи, протекающие соответственно во второй и первой катушках индуктивности в прототипе; u_C1np, u_C2nр - переменные напряжения соответственно на первом и втором конденсаторах в прототипе,

- уравнение вольт-амперной характеристики нелинейного устройства с отрицательным сопротивлением в прототипе, m₁ и m₀ - значения дифференциальных проводимостей среднего и боковых участков вольт-амперной характеристики нелинейного устройства с отрицательным сопротивлением в прототипе, U₀ - граничное напряжение между средним и боковыми участками вольт-амперной характеристики нелинейного устройства с отрицательным сопротивлением в прототипе, введением безразмерных переменных

и безразмерного времени

приводится к уравнениям

- безразмерная вольт-амперная характеристика нелинейного устройства с отрицательным сопротивлением в прототипе,

Таким образом, описывающие заявленный генератор безразмерные уравнения (3) и описывающие прототип безразмерные уравнения (6) отличаются лишь нелинейными функциями S(y-x) и h(y-x).In this case, the initial system of equations describing the prototype:

where R _np is the absolute value of the equivalent negative resistance of a linear device with negative resistance in the prototype; C1 _NP and C2 _NP - capacitance, respectively, of the first and second capacitors in the prototype; L1 _np and L2 _np - inductance, respectively, of the second and first coils of inductance in the prototype; i _L1np , i _L2np - alternating currents flowing respectively in the second and first inductors in the prototype; u _C1np , u _C2nр - alternating voltages respectively on the first and second capacitors in the prototype,

- the equation of the current-voltage characteristic of a nonlinear device with negative resistance in the prototype, m ₁ and m ₀ are the differential conductivities of the middle and side sections of the current-voltage characteristic of a nonlinear device with negative resistance in the prototype, U ₀ is the boundary voltage between the middle and side sections of the volt ampere characteristics of a nonlinear device with negative resistance in the prototype, the introduction of dimensionless variables

and dimensionless time

reduced to equations

- dimensionless current-voltage characteristic of a nonlinear device with negative resistance in the prototype,

Thus, the dimensionless equations (3) describing the claimed generator and the dimensionless equations describing the prototype (6) differ only in the nonlinear functions S (yx) and h (yx).

Если в системе уравнений (9) сделать замену переменных: х_k=х+2kc, z_k= z-2kc, w_k=w+2kc и учесть, что

(так как 2kc - константа, не зависящая от безразмерного времени τ), получим систему

которая ничем не отличается от системы безразмерных дифференциальных уравнений (6), описывающих динамику прототипа, так как функция

в системе уравнений (10) идентична функции h(y-x) в прототипе.As part of the dimensionless current-voltage characteristic S (yx), M + N + 1 segments h _k can be distinguished (see Fig. 4), where k = -M ...- 1, 0, 1 ... N. Moreover, the middle segment h ₀ is identical to the dimensionless current-voltage characteristic h (yx) of the device with negative resistance in the prototype, and the side segments can be obtained by moving the middle segment h ₀ along the dimensionless load line y-x by the interval [2kc, 2kc], that is the equation of any side segment can be expressed in terms of the equation of the mean: h _k (yx) = h ₀ (yx-kc) + kc. Therefore, within the kth segment h _k (at (2k-1) c-1 <yx <(2k + 1) c + 1) the generator dynamics can be described by a local system of differential equations:

If in the system of equations (9) we make a change of variables: x _k = x + 2kc, z _k = z-2kc, w _k = w + 2kc and take into account that

(since 2kc is a constant independent of the dimensionless time τ), we obtain the system

which is no different from the system of dimensionless differential equations (6) describing the dynamics of the prototype, since the function

in the system of equations (10) is identical to the function h (yx) in the prototype.

Therefore, for each of the segments h _k dimensionless current-voltage characteristics S (yx) the conditions for the excitation of chaotic oscillations are the same as in the prototype. Since the function S (yx) consists of such segments, this statement holds true for this function as a whole.

и k в системе уравнений (3) принадлежали области гиперхаотической динамики безразмерных уравнений (6), описывающих прототип.Thus, in order for the excitation of hyperchaotic oscillations to occur in the inventive generator, it is sufficient that the coefficients

and k in the system of equations (3) belonged to the region of hyperchaotic dynamics of dimensionless equations (6) describing the prototype.

раз по сравнению с прототипом (см. фиг.5 и 6).Like the function h (yx) in the prototype, each segment h _{k of the} function S (x) consists of a middle and two side sections, and two adjacent segments have a common side section (see figure 4). When the operating point is located within the lateral section belonging simultaneously to two adjacent segments, the dynamics of the system can be described simultaneously by two local systems of equations (10) corresponding to these neighboring segments. For certain values of the coefficients α, β, δ, λ, k, known from the properties of the prototype, each such system of equations determines the movement of the working point within all three sections of its segment. Therefore, the operating point located on the common side section of adjacent segments can, over time, go to the second side section of both one and the other neighboring segments. As a result, in system (3), the operating point moves within all segments of the function S (yx), which, all other things being equal, increases the size of the strange attractor in the inventive generator approximately

times compared with the prototype (see figure 5 and 6).

 And this gives an additional, in comparison with the prototype and analogues, the ability to control the parameters of the generated hyperchaotic signal by changing the geometry of the strange attractor while varying the number of segments of the volt-ampere characteristic of a non-linear device with negative resistance.

 Thus, when applying voltage to the circuit of a device with a negative resistance, the operating point occupies the initial position at the intersection of the load line with one of the side sections of a segment of the current-voltage characteristic of a non-linear device with negative resistance. Since an unstable singular point of the saddle-focus type corresponds to this position of the working point in the phase space of system (3), hyperchaotic self-oscillations appear in the generator. In this case, the working point moves within all M + N + 1 segments of the working section of the current-voltage characteristic.

 The condition for such operation of the claimed generator of hyperchaotic oscillations is the correspondence of the values of the coefficients α, β, δ, λ and k to such a regime of hyperchaotic oscillations in local equations (10), which is characterized by the fact that the operating point moves within all three sections of the corresponding current-voltage segment specifications. Since the local system of dimensionless equations (10) describing the claimed generator is identical to the dimensionless equations (6) describing the prototype, these values of the coefficients α, β, δ, λ, k are known from the properties of the prototype. Therefore, the values of the physical parameters of the claimed generator of hyperchaotic oscillations are selected from relations (4), (7), (8).

где R1 - сопротивление резистора 18 в первом четырехполюснике; R2 - значение сопротивлений резисторов 18 в остальных - со второго по 3+2Max(M,N)-й - четырехполюсниках, R3 - значение сопротивлений первого 8, второго 9, третьего 10 и четвертого 11 резисторов. При этом дифференциальные сопротивления среднего и боковых участков каждого сегмента вольт-амперной характеристики нелинейного устройства с отрицательным сопротивлением равны соответственно λR≈2R3-R1 и

Граничные токи между участками вольт-амперной характеристики нелинейного устройства с отрицательным сопротивлением, имеющими различные дифференциальные сопротивления, задаются генераторами токов, входящими в состав четырехполюсников.When all transistors are identical, a non-linear device with negative resistance has the current-voltage characteristic given in the claims if R1 ≈ R (1-λ),

where R1 is the resistance of the resistor 18 in the first four-terminal network; R2 - the value of the resistances of the resistors 18 in the rest - from the second to 3 + 2Max (M, N) -th - the four-terminal, R3 - the value of the resistances of the first 8, second 9, third 10 and fourth 11 resistors. In this case, the differential resistances of the middle and side sections of each segment of the volt-ampere characteristic of a non-linear device with negative resistance are equal to λR≈2R3-R1 and

The boundary currents between the sections of the volt-ampere characteristic of a non-linear device with a negative resistance having different differential resistances are set by the current generators included in the four-terminal devices.

 If we take for such a positive direction the alternating current i flowing through a non-linear device with negative resistance when it flows into the first output of this device and flows from its second output, then the current-voltage characteristic of a non-linear device with negative resistance will correspond to the equation given in the claims if the output currents of the current generators included in the four-terminal network have the following values.

At M = N, the output currents of the current generators 16 and 17 contained in the first four-terminal terminal 14 are I ₁ = (10 ... 20) I _KI , where I _KI is the value of the output currents of the current generators 27 and 28 contained in the impedance converters; the output currents of the current generators 16 and 17 contained in the rest - from the second to 3 + 2Max (M, N) -th - four-terminal, are equal to 2I _KI .

The case M> N differs from the case M = N in that the output currents of the first current generators 16 contained in the first and 3 + 2Nth quadrupole 14 are equal to 2I _KI and I _1, respectively.

The case N> M differs from the case M = N in that the output currents of the second current generators 17 contained in the first and 3 + 2Mth quadrupole 14 are 2I _KI and I _1, respectively.

Выходные токи первого 12 и второго 13 генераторов тока равны или больше 2I_КИ[1+Max(M,N)]+2I₁.Wherein

The output currents of the first 12 and second 13 current generators are equal to or greater than 2I _KI [1 + Max (M, N)] + 2I ₁ .

Electronic adjustment of the oscillation mode from the case corresponding to any one value of the numbers M and N to the case corresponding to other values of the numbers M and N is carried out by tuning the current generators of the four-terminal devices. In this case, the number of quadripoles is selected corresponding to the largest required values of the numbers M and N. To switch to the oscillation mode corresponding to some smaller numbers M * and N *, the output current of the first current generator 16, which is part of the 3 + 2M * 4th quadrupole, and the output the current of the second current generator 17, which is part of the 3 + 2N * -th four-terminal, is set equal to I ₁ , and the output currents of the first 16 and second 17 current generators included in the first four-terminal, are equal to 2I _KI .

 In this case, a nonlinear device with negative resistance operates as follows.

где

g₀ - эквивалентная проводимость последовательно включенных со второго по 3+2Max(M,N)-й четырехполюсников со стороны первого и второго выводов второго четырехполюсника. При значениях тока i, протекающего через выводы нелинейного устройства с отрицательным сопротивлением, лежащих в пределах интервала [-(c-1)I₀,(c-1)I₀], g₀≈g₂[1+Мах(М,N)]-g₂[1+Max(M,N)]=0, где

откуда R_Э≈2R3-R1. В это время рабочая точка находится в пределах среднего участка сегмента h₀ безразмерной вольт-амперной характеристики S(y-x). При выходе значения тока i за пределы интервала [-(с-1)I₀,(с-1)I₀] запирается первый 19 или второй 20 транзистор конвертора импеданса, входящего в состав 3+2Max(M,N)-го четырехполюсника. В результате проводимость g₀ становится равной g₀≈g₂Max(M,N)-g₂[1+Мах(М,N)]=-g₂, а эквивалентное сопротивление нелинейного устройства с отрицательным сопротивлением приобретает значение

При этом рабочая точка перемещается на один из боковых участков сегмента h₀. Когда значение тока i выходит за границы интервала [-(c+1)I₀,(c+1)I₀], запирается первый 19 или второй 20 транзистор конвертора импеданса, входящего в состав 2+2Мах(М,N)-го четырехполюсника, проводимость g₀ и сопротивление R_Э приобретают значения g₀≈g₂Max(M,N)-g₂Max(M,N)=0 и R_Э≈2R3-R1 соответственно, а рабочая точка переходит, в зависимости от направления тока i, на средний участок сегмента h₁ или h_-1. При выходе значения тока i за пределы интервала [-(3с-1)I₀, (3c-1)I₀] запирается первый 19 или второй 20 транзистор конвертора импеданса, входящего в состав 1+2Max(M,N)-го четырехполюсника, проводимость g₀ и сопротивление R_Э становятся равными соответственно g₃≈g₂[Max(M,N)-1]-g₂Max(M,N)=-g₂ и

а рабочая точка перемещается на внешний по отношению к началу координат боковой участок сегмента h₁ или h_-1, и так далее. При уменьшении величины тока i, протекающего через нелинейное устройство с отрицательным сопротивлением, все повторяется в обратном порядке.The equivalent resistance R _{E of a} non-linear device with a negative resistance is approximately equal to

Where

g ₀ is the equivalent conductivity of series-connected from the second to the 3 + 2Max (M, N) -th quadripoles from the side of the first and second terminals of the second quadrupole. For current i flowing through the terminals of a non-linear device with negative resistance lying within the interval [- (c-1) I ₀ , (c-1) I ₀ ], g ₀ ≈g ₂ [1 + Max (M, N )] - g ₂ [1 + Max (M, N)] = 0, where

whence R _e ≈2R3-R1. At this time, the operating point lies within the middle segment of the segment h _{0 of the} dimensionless current-voltage characteristic S (yx). When the current i exceeds the limits of the interval [- (s-1) I ₀ , (s-1) I ₀ ], the first 19 or second 20 transistor of the impedance converter included in the 3 + 2Max (M, N) -th quadrupole . As a result, the conductivity g ₀ becomes equal to g ₀ ≈g ₂ Max (M, N) -g ₂ [1 + Max (M, N)] = - g ₂ , and the equivalent resistance of a nonlinear device with negative resistance takes on the value

In this case, the working point moves to one of the side sections of the segment h ₀ . When the value of the current i goes beyond the limits of the interval [- (c + 1) I ₀ , (c + 1) I ₀ ], the first 19 or second 20 transistor of the impedance converter included in the 2 + 2Max (M, N) the quadripole, the conductivity g ₀ and the resistance R _Э acquire the values g ₀ ≈g ₂ Max (M, N) -g ₂ Max (M, N) = 0 and R _Э ≈2R3-R1, respectively, and the operating point goes over, depending on the direction of the current i, to the middle segment of the segment h ₁ or h _-1 . When the current i falls outside the interval [- (3s-1) I ₀ , (3c-1) I ₀ ], the first 19 or second 20 transistor of the impedance converter included in the 1 + 2Max (M, N) -th quadrupole , conductivity g ₀ and resistance R _E become equal respectively g ₃ ≈g ₂ [Max (M, N) -1] -g ₂ Max (M, N) = - g ₂ and

and the working point moves to the lateral segment of the segment h ₁ or h _-1 external to the coordinate origin, and so on. With a decrease in the current i flowing through a non-linear device with negative resistance, everything repeats in the reverse order.

 The increased temperature stability of the generated hyperchaotic signal is due to the fact that the equivalent negative resistance of a linear device with negative resistance and the current-voltage characteristic of a nonlinear device with negative resistance are practically independent of the parameters of the transistors due to the mutual compensation of the emitter resistances of the transistors 19 and 21, 22 and 23, 20 and 24, 25 and 26 in each impedance converter.

 Hyperchaotic oscillations in equations (10), characterized by the movement of the operating point within all three sections of each segment of the volt-ampere characteristic of a non-linear device with negative resistance, occur, in particular, at α≈10, β = 0.5 ... 0.7 , δ≈1.5, λ≈-0.2, k≈-15.

L1 = βR²C1 ≈ 0,13 Гн,

R1≈576 Ом, R2≈360 Ом, R3≈240 Oм.If we take R = 480 Ohm, C1 = 80 nF, then hyperchaotic oscillations in the claimed generator are observed at

L1 = βR ² C1 ≈ 0.13 H,

R1≈576 Ohm, R2≈360 Ohm, R3≈240 Ohm.

 The examples of the dimensionless strange attractor corresponding to these values of the generator parameters at M = 0, N = 1 and at M = N = 2 are shown in FIGS. 5 and 6, respectively. In FIG. Figures 7 and 8 show the corresponding examples of the dependence of the dimensionless variable w on time.

 In the case of M = 0, N = 1, the device with negative resistance contains five four-terminal devices, in the case of M = N = 2 - seven four-terminal devices.

Let I ₀ = 0.25 mA. The above values of the coefficients λ and k correspond to I _KI ≈0.4 mA. Moreover, in the case of M = 0, N = 1, the output currents of the first 16 and second 17 current generators contained in the second, fourth and fifth four-terminal networks, as well as the output current of the first current generator contained in the third four-terminal network, and the output current of the second current generator, contained in the first four-terminal network are equal to 2I _KI ≈0.8 mA. The output currents of the second current generator contained in the third four-terminal network and the first current generator contained in the first four-terminal network are I ₁ = 4 ... 8 mA.

In the case of M = N = 2, the device with negative resistance contains seven four-terminal devices. The output currents of the first and second current generators contained in the first four-terminal network are I ₁ = 4 ... 8 mA. The output currents of the first and second current generators contained in the remaining — from the second to the seventh — four-terminal devices are 2I _KI ≈0.8 mA.

In order to carry out electronic tuning from the case M = N = 2 to the case M = 0, N = 1 in a chaotic oscillator with a non-linear device with negative resistance and containing seven four-terminal devices, the output current of the second current generator contained in the fifth four-terminal should be increased, and the output current of the first current generator contained in the third four-terminal, to I ₁ = 4 ... 8 mA, and reduce the output currents of the first and second current generators contained in the first four-terminal, to 0.8 mA.

 Thus, the proposed generator of hyperchaotic oscillations compares favorably with the prototype and analogues in that it provides additional, in comparison with them, the ability to control the parameters of the generated hyperchaotic signal by changing the geometry of the strange attractor while varying the number of segments of the volt-ampere characteristic of a non-linear device with negative resistance.

Claims (2)

1. A generator of hyperchaotic oscillations, containing a linear and non-linear device with negative resistance, the first terminals of which are connected to the first terminal of the first capacitor, the second terminal of which is connected to the first terminal of the first inductor, the second terminal of which is connected to the second terminal of the non-linear device with negative resistance and the first the output of the second capacitor, the second output of which is connected to the first output of the second inductor, characterized in that the second output of the linear device Twa negative resistance connected to the second terminal of the first capacitor and the second terminal of the second inductor is connected to a first terminal of the first capacitor, wherein the operating portion of the current-voltage characteristic of a nonlinear device with negative resistance is defined by the equation

where u is the voltage that arises between the terminals of a nonlinear device with negative resistance under the action of current i flowing through them;
R is the absolute value of the equivalent negative resistance of a linear device with negative resistance;
I ₀ is the boundary current between the middle and adjacent side sections of the current-voltage characteristic of a nonlinear device with negative resistance;
λ and k are constants satisfying the relations λ <0, λk>1;

M and N are non-negative integers.  2. The generator of hyperchaotic oscillations according to claim 1, characterized in that the linear device with negative resistance contains a first impedance converter, the first and second input terminals of which are the corresponding first and second conclusions of a linear device with negative resistance, the first and second load terminals of the first impedance converter connected to the first terminals of the corresponding first and second resistors, the second terminals of which are connected to a common bus, a nonlinear device with a negative resistance it contains 3 + 2Max (M, N) series-connected four-terminal, where Max (M, N) is the larger of the numbers M and N, the first and second terminals of the first four-terminal are connected through the corresponding third and fourth resistors to the first and second terminals of the nonlinear device, respectively with negative resistance and outputs of the corresponding first and second current generators, the common buses of which are connected to the first power bus, the third and fourth outputs of each previous four-terminal are connected respectively to the first and second output for the subsequent four-terminal, each four-terminal contains an impedance converter, the first and second input terminals of which are the corresponding first and second terminals of the four-terminal, the first and second load terminals of the impedance converter, which are the third and fourth terminals of the four-terminal, connected to the corresponding first and second terminals of the resistor and the outputs the respective first and second quadrupole current generators, the common buses of which are connected to the second power bus, each The first impedance converter contains the first and second transistors, the emitters of which are the corresponding first and second input terminals of the impedance converter, the collector of the first transistor is connected to the emitter of the third transistor, whose collector, which is the first load terminal of the impedance converter, is connected to the base and collector of the fourth transistor, the emitter of which connected to the base of the third transistor and the collector of the fifth transistor, the base of which is connected to the collector of the second transistor and the emitter of the sixth a transistor whose collector, which is the second load terminal of the impedance converter, is connected to the base and collector of the seventh transistor, the emitter of which is connected to the base of the sixth transistor and the collector of the eighth transistor, the base of which is connected to the collector of the first transistor, the bases of the first and second transistors are connected to the emitters of the corresponding fifth and the eighth transistors and the outputs of the respective first and second current generators of the impedance converter, the common buses of which are connected to the first power bus.

Images