A chaotic circuit containing a composite power function

Abstract

The present invention discloses a chaotic circuit containing a composite power function. The circuit comprises an X signal channel, a Y signal channel, a ‑Y signal channel, and a Z signal channel, formed by first to seventh operational amplifiers, first to fourth analog multipliers, first to fourteen resistors, first to three capacitors, and a DC power supply. The outputs of each signal channel are interconnected via analog multipliers and resistors within each channel, generating a three-dimensional chaotic circuit state equation containing composite power function terms. This invention utilizes an uncommon construction method, increasing system complexity while requiring only a small number of operational amplifiers and multipliers, thereby reducing the difficulty of circuit implementation. This invention has significant implications for chaotic systems in information engineering fields such as communication encryption, radar encryption, and electronic countermeasures.

Description

Technical Field

[0001] The present invention relates to a chaotic circuit, in particular to a chaotic circuit containing a composite power function. Background Art

[0002] Chaos is a pseudo-random phenomenon generated by deterministic nonlinear systems. It exhibits initial value sensitivity and a continuous, wideband power spectrum. Chaotic systems are sensitive to initial conditions, are easy to generate, and difficult to predict and isolate using conventional time- and frequency-domain processing. This makes chaotic signals particularly suitable for secure communications and information encryption. Therefore, developing chaotic signal generator circuits with varying chaotic properties is crucial for the application of chaotic systems in information engineering fields such as communication encryption, radar encryption, and electronic countermeasures.

[0003] Nonlinearity is a necessary condition for a system to generate chaos. In a sense, the strength of nonlinearity determines the complexity of the chaotic system itself and its chaotic attractors. The nonlinear terms of typical Lorenz, Chen, and Lu systems are all composed of quadratic nonlinear functions. Generally, generating more novel chaotic attractors requires increasing system complexity, but this also increases the difficulty of system implementation. How to increase system complexity without increasing the complexity of system implementation is an important research topic. Summary of the Invention

[0004] In order to solve the technical problem in the prior art of increasing the complexity of the system while not increasing the complexity of the system implementation, the present invention provides a chaotic circuit containing a composite power function.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] The present invention provides a chaotic circuit containing a composite power function, comprising an X signal channel, a Y signal channel, a -Y signal channel, and a Z signal channel formed by first to seventh operational amplifiers, first to fourth analog multipliers, first to fourteen resistors, first to three capacitors, and a DC power supply. The output ends of the signal channels are connected via analog multipliers and resistors provided in each channel to generate a system state equation of a three-dimensional chaotic circuit having composite power function terms.

[0007] The X signal channel includes a first operational amplifier, a first capacitor, and a first resistor. The first resistor is connected to the inverting input terminal of the first operational amplifier. The inverting input terminal of the first operational amplifier is connected to its output terminal via the first capacitor, and the non-inverting input terminal of the first operational amplifier is grounded.

[0008] The Y signal and -Y signal channels include second to third operational amplifiers, a second capacitor, a first analog multiplier, and second to fifth resistors, wherein the second resistor is connected to the inverting input of the second operational amplifier, the inverting input of the second operational amplifier is connected to its output via the second capacitor, and the non-inverting input of the second operational amplifier is grounded; the output of the first analog multiplier is connected to the inverting input of the second operational amplifier via the fourth resistor, the output of the second operational amplifier is connected to the inverting input of the third operational amplifier via the fifth resistor, the inverting input of the third operational amplifier is connected to its output via the third resistor, and its non-inverting input is grounded; the output of the second operational amplifier is the Y signal output, and the output of the third operational amplifier is the -Y signal output.

[0009] The Z signal channel includes fourth to seventh operational amplifiers, a third capacitor, second to fourth analog multipliers, and sixth to fourteenth resistors, wherein the output terminal of the second analog multiplier is connected to the inverting input terminal of the fourth operational amplifier through the sixth resistor, and the non-inverting input terminal thereof is grounded. The inverting input terminal of the fourth operational amplifier is connected to its output terminal through the third capacitor; the eighth resistor and the tenth resistor are connected in parallel to the inverting input terminal of the fifth operational amplifier, the inverting input terminal of the fifth operational amplifier is connected to its output terminal through the ninth resistor, and the non-inverting input terminal thereof is grounded. The output terminal of the fifth operational amplifier is connected to the inverting input terminal of the sixth operational amplifier through the eleventh resistor, and the inverting input terminal of the sixth operational amplifier is connected to the inverting input terminal of the sixth operational amplifier through the twelfth resistor. The resistor is connected to its output end, and its non-inverting input end is grounded. The output end of the sixth operational amplifier is connected to the inverting input end of the seventh operational amplifier through the thirteenth resistor, and its non-inverting input end is grounded. The output end of the seventh operational amplifier is connected to the second input end of the fourth analog multiplier. The fourth analog multiplier is connected to the inverting input end of the seventh operational amplifier through the fourteenth resistor. The output end of the seventh operational amplifier is connected to the first and second input ends of the third analog multiplier. The output end of the third analog multiplier is connected to the first input end of the fourth analog multiplier. The output end of the seventh operational amplifier is connected to the inverting input end of the fourth operational amplifier through the seventh resistor. The output end of the fourth operational amplifier is the Z signal output end.

[0010] The Y signal output terminal is connected to the first resistor; the X signal output terminal is connected to the second resistor; the Y signal output terminal is connected to the eighth resistor; and the DC voltage source is connected to the inverting input terminal of the fifth operational amplifier through the tenth resistor.

[0011] The system state equation of the three-dimensional chaotic circuit of the compound power function term includes two quadratic terms and one compound power function term, as follows:

[0012]

[0013] Wherein, x, y, and z are the voltage values of the output terminals of the first, second, and fourth operator amplifiers, respectively.

[0014] The present invention has the following beneficial effects and advantages:

[0015] 1. The present invention provides a chaotic circuit containing a composite power function. The chaotic circuit consists of only five terms, one of which is a cube root term. This is a very rare construction method, which increases the complexity of the system. However, it can be implemented using fewer operational amplifiers and multipliers, thereby reducing the difficulty of circuit implementation.

[0016] 2. The present invention realizes a three-dimensional chaotic circuit through linear terms, quadratic cross terms and cube root terms, which has important significance for chaotic systems in information engineering fields such as communication encryption, radar encryption, and electronic countermeasures.

[0017] 3. The present invention has a simple structure and generates a small chaotic signal attraction domain. The circuit has good reference value and application prospects in chaotic signal generation and secure communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The electrical principle diagram of the composite power function chaotic circuit of the present invention;

[0019] Figure 2 This is the electrical schematic diagram of the X signal channel in the present invention;

[0020] Figure 3 Schematic diagram of the electrical principle of the Y signal channel and the -Y signal channel in the present invention;

[0021] Figure 4 This is the electrical schematic diagram of the Z signal channel in the present invention;

[0022] Figure 5 is a timing diagram of the X signal of the present invention;

[0023] Figure 6 It is the Y signal timing diagram of the present invention;

[0024] Figure 7 is a timing diagram of the Z signal of the present invention;

[0025] Figure 8 is the XY phase diagram of the present invention;

[0026] Figure 9 is the XZ phase diagram of the present invention;

[0027] Figure 10 It is the YZ phase diagram of the present invention.

[0028] Among them, U1~U7 are the first to seventh operational amplifiers, A1~A4 are the first to fourth analog multipliers, R1~R14 are the first to fourteenth resistors, C1~C3 are the first to third capacitors, and VCC is the first DC power supply. DETAILED DESCRIPTION

[0029] The present invention will be further described below with reference to the accompanying drawings.

[0030] like Figure 1 As shown, the present invention provides a chaotic circuit containing a composite power function, which is a three-dimensional chaotic circuit. It has an X signal channel, a Y signal channel, a -Y signal channel, and a Z signal channel formed by first to seventh operational amplifiers U1 to U7, first to fourth analog multipliers A1 to A4, first to fourteenth resistors R1 to R14, first to third capacitors C1 to C3, and a DC power supply VCC.

[0031] like Figure 2 As shown, the X signal channel includes: a first operational amplifier U1, a first capacitor C1, and a first resistor R1, wherein the first resistor R1 is connected to the inverting input terminal of the first operational amplifier U1, the inverting input terminal of the first operational amplifier U1 is connected to its output terminal through the first capacitor C1, and the non-inverting input terminal thereof is grounded;

[0032] like Figure 3 As shown, the Y signal and -Y signal channels include: second to third operational amplifiers U2 to U3, a second capacitor C2, a first analog multiplier A1, and second to fifth resistors R2 to R5, wherein the second resistor R2 is connected to the inverting input terminal of the second operational amplifier U2, the inverting input terminal of the second operational amplifier U2 is connected to its output terminal via the second capacitor C2, and the non-inverting input terminal of the second operational amplifier U2 is grounded; the output terminal of the first analog multiplier A1 is connected to the inverting input terminal of the second operational amplifier U2 via the fourth resistor R4, the output terminal of the second operational amplifier U2 is connected to the inverting input terminal of the third operational amplifier U3 via the fifth resistor R5, the inverting input terminal of the third operational amplifier U3 is connected to its output terminal via the third resistor R3, and the non-inverting input terminal of the third operational amplifier U3 is grounded, the output terminal of the second operational amplifier U2 is the Y signal output terminal, and the output terminal of the third operational amplifier U3 is the -Y signal output terminal.

[0033] like Figure 4As shown, the Z signal channel includes: fourth to seventh operational amplifiers U4 to U7, a third capacitor C3, second to fourth analog multipliers A2 to A4 and sixth to fourteenth resistors R6 to R14, wherein the output end of the second analog multiplier A2 is connected to the inverting input end of the fourth operational amplifier U4 through the sixth resistor R6, and its non-inverting input end is grounded, and the inverting input end of the fourth operational amplifier is connected to its output end through the third capacitor; the eighth resistor R8 and the tenth resistor R10 are connected in parallel to the inverting input end of the fifth operational amplifier U5, the inverting input end of the fifth operational amplifier U5 is connected to its output end through the ninth resistor R9, and its non-inverting input end is grounded, the output end of the fifth operational amplifier U5 is connected to the inverting input end of the sixth operational amplifier U6 through the eleventh resistor R11, and the inverting input end of the sixth operational amplifier U6 is connected to the inverting input end of the sixth operational amplifier U6. The output terminal of the sixth operational amplifier U6 is connected to the inverting input terminal of the seventh operational amplifier U7 through the thirteenth resistor R13, and the inverting input terminal of the seventh operational amplifier U7 is grounded. The output terminal of the seventh operational amplifier U7 is connected to the second input terminal of the fourth analog multiplier A4. The fourth analog multiplier A4 is connected to the inverting input terminal of the seventh operational amplifier U7 through the fourteenth resistor R14. The output terminal of the seventh operational amplifier U7 is connected to the first and second input terminals of the third analog multiplier A3. The output terminal of the third analog multiplier A3 is connected to the first input terminal of the fourth analog multiplier A4. The output terminal of the seventh operational amplifier U7 is connected to the inverting input terminal of the fourth operational amplifier U4 through the seventh resistor R7. The output terminal of the fourth operational amplifier U4 is the Z signal output terminal.

[0034] In this embodiment, Figure 1 The circuit shown is divided into three functional modules. The first functional module implements the X signal channel, the second functional module implements the Y signal and -Y signal channels, and the third functional module implements the Z signal.

[0035] The electrical schematic diagram of the first functional module is as follows Figure 2 As shown, the curve of X signal changing with time is as follows Figure 5 As shown;

[0036] The electrical schematic diagram of the second functional module is as follows Figure 3 As shown, the curve of Y signal changing with time is as follows Figure 6 As shown;

[0037] The electrical schematic diagram of the third functional module is as follows Figure 4 As shown, the curve of Z signal changing with time is as follows Figure 7 As shown;

[0038] From the above Figures 5-7 It can be seen from the three time series curves that the solution of this system is non-periodic, reflecting the inherent randomness of chaos.

[0039] Figure 8 shows an XY phase diagram, Figure 9 shows the XZ phase diagram, Figure 10 The YZ phase diagram is shown.

[0040] From the above Figures 8-10 It can be seen from the three phase diagrams that this chaotic attractor must be bounded, its motion trajectory is always confined to a certain area, and will not go out of the chaotic attraction domain.

[0041] In this embodiment, the voltage of the first DC power supply VCC is 12V; the multiples of the first to fourth analog multipliers A1 to A4 are all 0.1, the inverting power supply VEE of the first to seventh operational amplifiers U1 to U7 is -12V, and the non-inverting power supply VCC is 12V.

[0042] The component parameters in the embodiment are as follows:

[0043] R1=10KΩ, R2=5kΩ, R3=10KΩ, R4=0.083KΩ, R5=10KΩ, R6=0.33KΩ, R7=10KΩ, R8=10KΩ, R9=10KΩ, R10=12KΩ, R11=10KΩ, R12=10KΩ, R13=100KΩ, R14=1KΩ.

[0044] C1=C2=C3=0.1μF.

[0045] The first to fourth analog multipliers A1 to A4 are all AD633JRZ models. The first to seventh operational amplifiers U1 to U7 are all TL081ACD models.

[0046] The present invention constructs a complex three-dimensional chaotic system using simple linear terms, quadratic cross terms, and composite power function terms. The system state equation of the three-dimensional chaotic circuit of the present invention is:

[0047]

[0048] Wherein, x, y, and z are the voltage values of the output terminals of the first, second, and fourth operator amplifiers, respectively.

[0049] The chaotic circuit in the present invention is composed of only five terms, one of which is a cube root term. This is a relatively rare configuration, which increases the complexity of the system. However, it can be implemented using fewer operational amplifiers and multipliers, thereby reducing the difficulty of circuit implementation.

[0050] It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the scope of protection of the present invention.

Claims

1. A chaotic circuit containing a composite power function, characterized in that: The system comprises an X signal channel, a Y signal channel, a -Y signal channel, and a Z signal channel formed by first to seventh operational amplifiers, first to fourth analog multipliers, first to fourteenth resistors, first to third capacitors, and a DC power supply, wherein the output ends of the signal channels are connected via analog multipliers and resistors provided in each channel to generate a system state equation of a three-dimensional chaotic circuit having a composite power function term; The system state equation of the three-dimensional chaotic circuit of the compound power function term includes two quadratic terms and one compound power function term, as follows: (1) Where x, y, and z are the voltage values at the output terminals of the first, second, and fourth operator amplifiers, respectively; The X signal channel includes a first operational amplifier, a first capacitor, and a first resistor, wherein the first resistor is connected to the inverting input terminal of the first operational amplifier, the inverting input terminal of the first operational amplifier is connected to the output terminal thereof via the first capacitor, and the non-inverting input terminal thereof is grounded; The Y signal and -Y signal channels include second to third operational amplifiers, a second capacitor, a first analog multiplier, and second to fifth resistors, wherein the second resistor is connected to the inverting input of the second operational amplifier, the inverting input of the second operational amplifier is connected to its output via the second capacitor, and the non-inverting input of the second operational amplifier is grounded; the output of the first analog multiplier is connected to the inverting input of the second operational amplifier via the fourth resistor, the output of the second operational amplifier is connected to the inverting input of the third operational amplifier via the fifth resistor, the inverting input of the third operational amplifier is connected to its output via the third resistor, and the non-inverting input of the third operational amplifier is grounded; the output of the second operational amplifier is a Y signal output, and the output of the third operational amplifier is a -Y signal output. The Z signal channel includes fourth to seventh operational amplifiers, a third capacitor, second to fourth analog multipliers, and sixth to fourteenth resistors, wherein the output of the second analog multiplier is connected to the inverting input of the fourth operational amplifier via the sixth resistor, and the non-inverting input of the fourth operational amplifier is grounded. The inverting input of the fourth operational amplifier is connected to its output via the third capacitor. The eighth resistor and the tenth resistor are connected in parallel to the inverting input of the fifth operational amplifier. The inverting input of the fifth operational amplifier is connected to its output via the ninth resistor, and the non-inverting input of the fifth operational amplifier is grounded. The output of the fifth operational amplifier is connected to the inverting input of the sixth operational amplifier via the eleventh resistor, and the inverting input of the sixth operational amplifier is connected via the twelfth resistor. The resistor is connected to its output end, and its non-inverting input end is grounded. The output end of the sixth operational amplifier is connected to the inverting input end of the seventh operational amplifier through the thirteenth resistor, and its non-inverting input end is grounded. The output end of the seventh operational amplifier is connected to the second input end of the fourth analog multiplier. The fourth analog multiplier is connected to the inverting input end of the seventh operational amplifier through the fourteenth resistor. The output end of the seventh operational amplifier is connected to the first and second input ends of the third analog multiplier. The output end of the third analog multiplier is connected to the first input end of the fourth analog multiplier. The output end of the seventh operational amplifier is connected to the inverting input end of the fourth operational amplifier through the seventh resistor. The output end of the fourth operational amplifier is the Z signal output end.

2. The chaotic circuit containing a composite power function according to claim 1, characterized in that: The Y signal output terminal is connected to the first resistor; the X signal output terminal is connected to the second resistor; the Y signal output terminal is connected to the eighth resistor; and the DC voltage source is connected to the inverting input terminal of the fifth operational amplifier through the tenth resistor.

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