CN103414550A - Four-dimensional hyper-chaotic circuit - Google Patents

Abstract

The invention discloses a four-dimensional hyper-chaotic circuit which comprises a first channel circuit, a second channel circuit, a third channel circuit and a fourth channel circuit. The first channel circuit is composed of a multiplier A1, an inverter U1A, an inverting integrator U2A, an inverter U3A, a resistor R11, a resistor R12, a resistor R13, a resistor R14, a resistor Rx1, a resistor Rx2, a resistor Rx3 and a capacitor C1. The second channel circuit is composed of a multiplier A2, an inverter U4A, an inverting integrator U5A, a resistor R 21, a resistor R22, a resistor Ry1, a resistor Ry2 and a capacitor C2. The third channel circuit is composed of a multiplier A3, an inverter U6A, an inverting integrator U7A, a resistor R31, a resistor R32, a resistor Rz1, a resistor Rz2, a resistor Rz3 and a capacitor C3. The fourth channel circuit is composed of a multiplier A4, a multiplier A5, an inverter U8A, an inverting integrator U9A, a resistor 41, a resistor R42, a resistor Rw1, a resistor Rw2, a resistor Rw3 and a capacitor C4. According to the four-dimensional hyper-chaotic circuit, chaos evolving curves with different characteristics can be output and a hyper-chaotic secret communication system can be formed.

Description

A kind of four-dimensional hyperchaotic circuit

Technical field

The invention belongs to nonlinear circuit, often claim chaos circuit, be specifically related to a kind of four-dimensional hyperchaotic circuit.

Background technology

Chaos has disclosed true rule and the essential characteristic of non linear system motion, has reacted the dynamic behavior of system.Due to the randomlikeness of chaotic signal, continuous wide band power spectrum characteristic, the chaos system sensitive dependence to initial condition, and be easy to produce, be difficult to process prediction and the characteristics such as separate by time domain commonly used and frequency domain, make chaotic signal be specially adapted to the fields such as secure communication and information encryption.Therefore, realize having the chaotic signal generating circuit of different chaotic characteristics, chaos system is had great importance in information engineering fields such as communication encryption, radar communication, electronic countermeasuress.

Summary of the invention

The purpose of this invention is to provide the chaotic signal generating circuit that a kind of reliability and stability are better, interference free performance is higher.

The technical solution adopted in the present invention is:

A kind of four-dimensional hyperchaotic circuit, by first, second, the third and fourth channel circuit forms, the first passage circuit is by multiplier A1, inverter U1A, inverting integrator U2A, inverter U3A and resistance R 11, R12, R13, R14, Rx1, Rx2, Rx3 and capacitor C 1 form, the second channel circuit is by multiplier A2, inverter U4A, inverting integrator U5A and resistance R 21, R22, Ry1, Ry2 and capacitor C 2 form, the third channel circuit is by multiplier A3, inverter U6A, inverting integrator U7A and resistance R 31, R32, Rz1, Rz2, Rz3 and capacitor C 3 form, the four-way circuit is by multiplier A4 and A5, inverter U8A, inverting integrator U9A and resistance R 41, R42, Rw1, Rw2, Rw3 and capacitor C 4 form, the output signal of first passage circuit feeds back to input, contact resistance Rx2 is as a road input signal, this output signal is also as the mono-road input signal of multiplier A2De in the second channel circuit, also connect multiplier A3 and act on the third channel circuit, this output signal also connects multiplier A5 and acts on the four-way circuit, the output signal of second channel circuit feeds back to input, contact resistance Ry1 acts on the second channel circuit, also connect multiplier A1 and act on the first passage circuit, this output signal also connects multiplier A3 and acts on the third channel circuit, also connects multiplier A4 and acts on the four-way circuit, the output signal of third channel circuit feeds back to input, contact resistance Rz2 acts on the third channel circuit, this output signal is also as the mono-road input signal of multiplier A1De in the first passage circuit, this output signal also connects multiplier A2 and acts on the second channel circuit, also connects multiplier A4 and multiplier A5 acts on the four-way circuit, the output signal of four-way circuit feeds back to input, and contact resistance Rw3 acts on the four-way circuit, goes back contact resistance Rz3 and acts on the third channel circuit, and this output signal also contact resistance Rx3 acts on the first passage circuit.

In the first passage circuit, multiplier A1 is connected with 1 pin of inverter U1A by resistance R x1; 1 pin connects 5 pins of inverter U1A by resistance R 11,5 pins are connected with 6 pins of inverter U2A by resistance R 12; Resistance R x2 is connected with described 6 pins; Resistance R x3 is connected with 11 pins of inverter U3A, and 11 pins connect 15 pins of inverter U3A by resistance R 13, and 15 pins are connected with described 6 pins by resistance R 14; 6 pins are connected with 10 pins of inverter U2A by capacitor C 1; 2 pins of inverter U1A and 7 pins of inverter U2A, 12 pin ground connection; 13 pins, 14 pins of 8 pins of 3 pins of inverter U1A, 4 pins and inverter U2A, 9 pins and inverter U3A meet VCC.

In the second channel circuit, multiplier A2 is connected with 6 pins of inverter U5A by resistance R y2; Resistance R y1 connects 1 pin of inverter U4A, and 1 pin connects 5 pins of inverter U5A by resistance R 21, and 5 pins are connected with 6 pins of inverter U5A by resistance R 22; 6 pins are connected with 10 pins of inverter U5A by capacitor C 2; The 7 pin ground connection of 2 pins of inverter U4A and inverter U5A; 8 pins, 9 pins of 3 pins of inverter U4A, 4 pins and inverter U5A meet VCC.

In the third channel circuit, multiplier A3 is connected with 1 pin of inverter U6A by resistance R z1; 1 pin connects 5 pins of inverter U6A by resistance R 31,5 pins are connected with 6 pins of inverter U7A by resistance R 32; Resistance R z2 is connected with described 6 pins; Resistance R z3 is connected with described 6 pins; 6 pins are connected with 10 pins of inverter U7A by capacitor C 3; The 7 pin ground connection of 2 pins of inverter U6A and inverter U7A; 8 pins, 9 pins of 3 pins of inverter U6A, 4 pins and inverter U7A meet VCC.

In the four-way circuit, multiplier A4 is connected with 1 pin of inverter U8A by resistance R w1; 1 pin connects 5 pins of inverter U8A by resistance R 41,5 pins are connected with 6 pins of inverter U9A by resistance R 42; Multiplier A5 is connected with described 6 pins by resistance R w2; Resistance R w3 is connected with described 6 pins; 6 pins are connected with 10 pins of inverter U9A by capacitor C 4; The 7 pin ground connection of 2 pins of inverter U8A and inverter U9A; 8 pins, 9 pins of 3 pins of inverter U8A, 4 pins and inverter U9A meet VCC.

In the first passage circuit, inverting integrator U2A output is the X signal; In the second channel circuit, inverting integrator U5A output is Y-signal; In the third channel circuit, inverting integrator U7A output is the Z signal; In the four-way circuit, inverting integrator U9A output is the W signal; In the first passage circuit, capacitor C 1 is 1 μ F; In the second channel circuit, capacitor C 2 is 1 μ F; In the third channel circuit, capacitor C 3 is 1 μ F; In the four-way circuit, capacitor C 4 is 1 μ F.

The present invention is a kind of novel four-dimensional hyperchaotic circuit, can export the chaos with different qualities and develop curve, and can form the hyperchaos secret signalling, has good anti-interference.

The accompanying drawing explanation

Fig. 1 is the bifurcation graphs that system of the present invention changes with parameter a;

Fig. 2 is the x sequential chart of system parameters a=1 of the present invention;

Fig. 3 is the y sequential chart of system parameters a=1 of the present invention;

Fig. 4 is the z sequential chart of system parameters a=1 of the present invention;

Fig. 5 is the w sequential chart of system parameters a=1 of the present invention;

Fig. 6 is circuit diagram of the present invention;

Fig. 7 is X-Y phasor of the present invention;

Fig. 8 is X-Z phasor of the present invention;

Fig. 9 is X-W phasor of the present invention;

Figure 10 is Y-Z phasor of the present invention;

Figure 11 is Y-W phasor of the present invention;

Figure 12 is Z-W phasor of the present invention.

Embodiment

The present invention relates to a kind of four-dimensional hyperchaotic circuit, the signal application with strong chaotic characteristic of this circuit generation, in secure communication and image concealing, can be improved to the security performance of useful signal and the anti-ability of cracking of enhancing secrecy system.

System dimensionless mathematics model involved in the present invention is as follows:

$\left\{\begin{array}{c}\frac{\mathrm{dx}}{\mathrm{d\τ}}=-17x+4.95\mathrm{yz}+4w,\\ \frac{\mathrm{dy}}{\mathrm{d\τ}}=\mathrm{ay}-\mathrm{xz},\\ \frac{\mathrm{dz}}{\mathrm{d\τ}}=-6z+\mathrm{xy}-5w,\\ \frac{\mathrm{dw}}{\mathrm{d\τ}}=-\mathrm{xz}+5\mathrm{yz}-w.\end{array}\right.---\left(1\right)$

In formula (1), x, y, z, w are state variable, a is the parameter of the differential equation.Change parameter a ∈ [0,10], the bifurcation graphs that the system of the present invention as shown in Figure 1 of obtaining changes with parameter a.When choosing parameter a=1, obtain respectively the x as Fig. 2, Fig. 3, systematic shown in Figure 4 and Figure 5 (1), y, z, the w sequential chart now is transformed to circuit equation by system dimensionless mathematics model (1) involved in the present invention and is:

$\left\{\begin{array}{c}\frac{\mathrm{dX}}{\mathrm{dt}}=-\frac{1}{C_1{R}_{x2}}X+\frac{1}{C_1{R}_{12}}\mathrm{YZ}+\frac{1}{C_1{R}_{14}}W,\\ \frac{\mathrm{dY}}{\mathrm{dt}}=-\frac{1}{C_2{R}_{22}}Y-\frac{1}{{\text{C}}_2{R}_{y2}}\mathrm{XZ},\\ \frac{\mathrm{dZ}}{\mathrm{dt}}=-\frac{1}{C_3{R}_{z2}}Z+\frac{1}{C_3{R}_{32}}\mathrm{XY}-\frac{1}{C_3{R}_{z3}}W,\\ \frac{\mathrm{dW}}{\mathrm{dt}}=-\frac{1}{C_4{R}_{w2}}\mathrm{XZ}+\frac{1}{C_4{R}_{42}}\mathrm{YZ}-\frac{1}{C_4{R}_{w3}}W.\end{array}\right.---\left(2\right)$

In formula (2), X, Y, Z, W are four chaotic signals that the present invention exports, and X, Y, and Z, tetra-chaotic signals of W have the voltage dimension.Make that E is constant voltage, have voltage guiding principle amount, and x=X/E, y=Y/E, z=Z/E, w=W/E are arranged, obvious x, y, z, w is characteristic.Make τ=t/ τ ₀, τ ₀For the unit interval constant, by relatively (1) formula and (2) formula can obtain 1/C ₁R _X2=17/ τ ₀, 1/C ₁R ₁₂=4.95/ τ ₀, 1/C ₁R ₁₄=4/ τ ₀, 1/C ₂R ₂₂=1/ τ ₀, 1/C ₂R _Y2=1/ τ ₀, 1/C ₃R _Z2=6/ τ ₀, 1/C ₃R ₃₂=1/ τ ₀, 1/C ₃R _Z3=5/ τ ₀, 1/C ₄R _W2=1/ τ ₀, 1/C ₄R ₄₂=5/ τ ₀, 1/C ₄R _W3=1/ τ ₀, C wherein ₁=1 μ F, C ₂=1 μ F, C ₃=1 μ F, C ₄=1 μ F.

Circuit involved in the present invention is by first, second, third and the four-way the electric circuit constitute, and first, second, third, fourth channel circuit is realized respectively first, second, third, fourth function in formula (2).

The first passage circuit is comprised of multiplier A1, inverter U1A, inverting integrator U2A, inverter U3A and resistance R 11, R12, R13, R14 and Rx1, Rx2, Rx3.Wherein, multiplier A1 is connected with 1 pin of U1A by resistance R x1; 1 pin connects 5 pins by resistance R 11, and 5 pins are connected with 6 pins of U2A by resistance R 12; Resistance R x2 is connected with 6 pins; Resistance R x3 is connected with 11 pins of U3A, and 11 pins connect 15 pins by resistance R 13, and 15 pins are connected with 6 pins by resistance R 14; 6 pins are connected with 10 pins of U2A by capacitor C 1; 2 pins, 7 pins and 12 pin ground connection; 3 pins, 4 pins, 8 pins, 9 pins, 13 pins and 14 pins meet VCC.

The second channel circuit is comprised of multiplier A2, inverter U4A, inverting integrator U5A and resistance R 21, R22 and Ry1, Ry2.Wherein, multiplier A2 is connected with 6 pins of U5A by resistance R y2; Resistance R y1 connects 1 pin of U4A, and 1 pin connects 5 pins by resistance R 21, and 5 pins are connected with 6 pins of U5A by resistance R 22; 6 pins are connected with 10 pins of U5A by capacitor C 2; 2 pins and 7 pin ground connection; 3 pins, 4 pins, 8 pins and 9 pins meet VCC.

The third channel circuit is by multiplier A3, inverter U6A, inverting integrator U7A and resistance R 31, R32 and Rz1, Rz2, Rz3.Wherein, multiplier A3 is connected with 1 pin of U6A by resistance R z1; 1 pin connects 5 pins by resistance R 31, and 5 pins are connected with 6 pins of U7A by resistance R 32; Resistance R z2 is connected with 6 pins; Resistance R z3 is connected with 6 pins; 6 pins are connected with 10 pins of U7A by capacitor C 3; 2 pins and 7 pin ground connection; 3 pins, 4 pins, 8 pins and 9 pins meet VCC.

The four-way circuit is comprised of multiplier A4 and A5, inverter U8A, inverting integrator U9A and resistance R 41, R42 and Rw1, Rw2, Rw3.Wherein, multiplier A4 is connected with 1 pin of U8A by resistance R w1; 1 pin connects 5 pins by resistance R 41, and 5 pins are connected with 6 pins of U9A by resistance R 42; Multiplier A5 is connected with 6 pins of U9A by resistance R w2; Resistance R w3 is connected with 6 pins; 6 pins are connected with 10 pins of U9A by capacitor C 4; 2 pins and 7 pin ground connection; 3 pins, 4 pins, 8 pins and 9 pins meet VCC.

The output signal of first passage circuit feeds back to input, contact resistance Rx2 is as a road input signal, this output signal is also as the mono-road input signal of multiplier A2De in the second channel circuit, also connect multiplier A3 and act on the third channel circuit, this output signal also connects multiplier A5 and acts on the four-way circuit; The output signal of second channel circuit feeds back to input, contact resistance Ry1 acts on the second channel circuit, also connect multiplier A1 and act on the first passage circuit, this output signal also connects multiplier A3 and acts on the third channel circuit, also connects multiplier A4 and acts on the four-way circuit; The output signal of third channel circuit feeds back to input, contact resistance Rz2 acts on the third channel circuit, this output signal is also as the mono-road input signal of multiplier A1De in the first passage circuit, this output signal also connects multiplier A2 and acts on the second channel circuit, also connects multiplier A4 and multiplier A5 acts on the four-way circuit; The output signal of four-way circuit feeds back to input, and contact resistance Rw3 acts on the four-way circuit, goes back contact resistance Rz3 and acts on the third channel circuit, and this output signal also contact resistance Rx3 acts on the first passage circuit.In circuit, resistance capacitance is standard component, and the model of amplifier is LT082CM; The numerical value of VCC is 15V.

In the first passage circuit, inverting integrator U2A output is the X signal; In the second channel circuit, inverting integrator U5A output is Y-signal; In the third channel circuit, inverting integrator U7A output is the Z signal; In the four-way circuit, inverting integrator U9A output is the W signal; In the first passage circuit, capacitor C 1 is 1 μ F; In the second channel circuit, capacitor C 2 is 1 μ F; In the third channel circuit, capacitor C 3 is 1 μ F; In the four-way circuit, capacitor C 4 is 1 μ F.

X output, Y output, Z output and W output in Fig. 6 are connected to the oscilloscope signal input, the oscillogram that can show X, Y, Z and W, X-Y output phasor signal as shown in Figure 7, X-Z output phasor signal as shown in Figure 8, X-W output phasor signal as shown in Figure 9, as shown in figure 10, as shown in figure 11, Z-W output phasor signal as shown in figure 12 for Y-W output phasor signal for Y-Z output phasor signal.By Fig. 7, to Figure 12, proved validity of the present invention.

Claims (7)

1. four-dimensional hyperchaotic circuit, it is characterized in that: this circuit is comprised of four channel circuits: the first passage circuit is by multiplier A1, inverter U1A, inverter U2A, inverter U3A and resistance R 11, resistance R 12, resistance R 13, resistance R 14, resistance R x1, resistance R x2, resistance R x3 and capacitor C 1 form, the second channel circuit is by multiplier A2, inverter U4A, inverter U5A and resistance R 21, resistance R 22, resistance R y1, resistance R y2 and capacitor C 2 form, the third channel circuit is by multiplier A3, inverter U6A, inverter U7A and resistance R 31, resistance R 32, resistance R z1, resistance R z2, resistance R z3 and capacitor C 3 form, the four-way circuit is by multiplier A4, multiplier A5, inverter U8A, inverter U9A and resistance R 41, resistance R 42, resistance R w1, resistance R w2, resistance R w3 and capacitor C 4 form, the output signal of first passage circuit feeds back to input, contact resistance Rx2 is as a road input signal, this output signal is also as the mono-road input signal of multiplier A2De in the second channel circuit, also connect multiplier A3 and act on the third channel circuit, this output signal also connects multiplier A5 and acts on the four-way circuit, the output signal of second channel circuit feeds back to input, contact resistance Ry1 acts on the second channel circuit, also connect multiplier A1 and act on the first passage circuit, this output signal also connects multiplier A3 and acts on the third channel circuit, also connects multiplier A4 and acts on the four-way circuit, the output signal of third channel circuit feeds back to input, contact resistance Rz2 acts on the third channel circuit, this output signal is also as the mono-road input signal of multiplier A1De in the first passage circuit, this output signal also connects multiplier A2 and acts on the second channel circuit, also connects multiplier A4 and multiplier A5 acts on the four-way circuit, the output signal of four-way circuit feeds back to input, and contact resistance Rw3 acts on the four-way circuit, goes back contact resistance Rz3 and acts on the third channel circuit, and this output signal also contact resistance Rx3 acts on the first passage circuit.

2. a kind of four-dimensional hyperchaotic circuit according to claim 1 is characterized in that: in described first passage circuit, multiplier A1 is connected with 1 pin of inverter U1A by resistance R x1; 1 pin connects 5 pins of inverter U1A by resistance R 11,5 pins are connected with 6 pins of inverter U2A by resistance R 12; Resistance R x2 is connected with described 6 pins; Resistance R x3 is connected with 11 pins of inverter U3A, and 11 pins connect 15 pins of inverter U3A by resistance R 13, and 15 pins are connected with described 6 pins by resistance R 14; 6 pins are connected with 10 pins of inverter U2A by capacitor C 1; 2 pins of inverter U1A and 7 pins of inverter U2A, 12 pin ground connection; 13 pins, 14 pins of 8 pins of 3 pins of inverter U1A, 4 pins and inverter U2A, 9 pins and inverter U3A meet VCC.

3. a kind of four-dimensional hyperchaotic circuit according to claim 1 is characterized in that: in described second channel circuit, multiplier A2 is connected with 6 pins of inverter U5A by resistance R y2; Resistance R y1 connects 1 pin of inverter U4A, and 1 pin connects 5 pins of inverter U5A by resistance R 21, and 5 pins are connected with 6 pins of inverter U5A by resistance R 22; 6 pins are connected with 10 pins of inverter U5A by capacitor C 2; The 7 pin ground connection of 2 pins of inverter U4A and inverter U5A; 8 pins, 9 pins of 3 pins of inverter U4A, 4 pins and inverter U5A meet VCC.

4. a kind of four-dimensional hyperchaotic circuit according to claim 1 is characterized in that: in described third channel circuit, multiplier A3 is connected with 1 pin of inverter U6A by resistance R z1; 1 pin connects 5 pins of inverter U6A by resistance R 31,5 pins are connected with 6 pins of inverter U7A by resistance R 32; Resistance R z2 is connected with described 6 pins; Resistance R z3 is connected with described 6 pins; 6 pins are connected with 10 pins of inverter U7A by capacitor C 3; The 7 pin ground connection of 2 pins of inverter U6A and inverter U7A; 8 pins, 9 pins of 3 pins of inverter U6A, 4 pins and inverter U7A meet VCC.

5. a kind of four-dimensional hyperchaotic circuit according to claim 1 is characterized in that: in described four-way circuit, multiplier A4 is connected with 1 pin of inverter U8A by resistance R w1; 1 pin connects 5 pins of inverter U8A by resistance R 41,5 pins are connected with 6 pins of inverter U9A by resistance R 42; Multiplier A5 is connected with described 6 pins by resistance R w2; Resistance R w3 is connected with described 6 pins; 6 pins are connected with 10 pins of inverter U9A by capacitor C 4; The 7 pin ground connection of 2 pins of inverter U8A and inverter U9A; 8 pins, 9 pins of 3 pins of inverter U8A, 4 pins and inverter U9A meet VCC.

6. a kind of four-dimensional hyperchaotic circuit according to claim 1, it is characterized in that: in described first passage circuit, inverter U2A output is the X signal; In described second channel circuit, inverter U5A output is Y-signal; In described third channel circuit, inverter U7A output is the Z signal; In described four-way circuit, inverter U9A output is the W signal.

7. a kind of four-dimensional hyperchaotic circuit according to claim 1, it is characterized in that: in described first passage circuit, capacitor C 1 is 1 μ F; In described second channel circuit, capacitor C 2 is 1 μ F; In described third channel circuit, capacitor C 3 is 1 μ F; In described four-way circuit, capacitor C 4 is 1 μ F.

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