Improved Chua's system and FPGA-based Chua's chaotic signal generator thereof

A technology of Chua's system and chaotic signal, applied in the field of Chua's system and its FPGA-based Chua's chaotic signal generator, which can solve the problems of limited effect and sensitive initial value of chaotic system.

Pending Publication Date: 2021-03-12
CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY
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Problems solved by technology

Moreover, the current hardware implementation of multi-scroll chaotic systems (including typical Chua's systems) mainly adopts two methods of realizing chaos in analog circuits, namely, discrete component circuit design and chip integrated circuit design. Because discrete components are easily affected by temperature and aging Affected by environmental factors such as environmental factors, the chaotic system is extremely sensitive to the initial value, so the effect of using discrete component circuits to realize the chaotic system is very limited

Method used

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  • Improved Chua's system and FPGA-based Chua's chaotic signal generator thereof
  • Improved Chua's system and FPGA-based Chua's chaotic signal generator thereof
  • Improved Chua's system and FPGA-based Chua's chaotic signal generator thereof

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Effect test

no. 1 example ；

[0039] refer to Figure 1 to Figure 7 , providing an improved Chua's system, the state equation of this Chua's system is:

[0040]

[0041] Among them, x, y, z are system variables of Chua's system, α, β are system parameters, h(x) is a compound hyperbolic tangent cubic nonlinear function, h(x)=ax-b tan h(x 3 ), a is a fixed value, and b is a parameter to control the number of scrolls. Compared with the typical Chua's system, the Chua's system provided in this embodiment uses a compound hyperbolic tangent cubic nonlinear function, so that the Chua's system has richer dynamic behaviors than the typical Chua's system.

[0042] As an optional implementation, when the initial value of Chua's system is [0.5,0,0], system parameters α=8, β=12, a=0.3, figure 1 It shows the phase diagram of Chua's system simulated by using MATLAB respectively with control parameters b=0.4, b=0.5 and b=0.65, and realizes the numerical simulation results of one to three scroll Chua's attractors thro...

Embodiment approach

[0057] As an optional implementation, the system variables can be added with corresponding offset variables, so as to realize the chaotic attractor offset. Let the offset variable of variable x be k 1 , the offset variable of variable y is k 2 , the offset variable of variable z is k 3 , then the state variables x, y, z can be divided by x+k 1 ,y+k 2 ,z+k 3 replaced. The offset variable is free to be raised to any position, thus becoming a bipolar or unipolar signal. In this Chua's system, different attractors can be lifted to any position of the equilibrium plane by setting an appropriate value of the system parameter b, and then adding an offset variable to the state variable. To provide an implementation, considering the offset promotion of the state variable x, the state equation is as follows:

[0058]

[0059] When the initial value is [0.5,0,0], system parameters α=8, β=12, a=0.3, Figure 6 Shifts of one to three scroll chaotic attractors are shown for parame...

no. 2 example ；

[0065] refer to Figure 8 to Figure 11 , provide a multi-scroll Chua's chaotic signal generator based on FPGA design, which is used to make the above-mentioned improved Chua's system output chaotic signals. Here, use XilinxVirtex-6 (ZYNQ-XC7Z020) FPGA development board to build this chaotic generator The overall architecture of this multi-volume Chua's chaotic signal generator includes: Chua's oscillator, control unit and analog converter (DAC), of which:

[0066] The above-mentioned Chua's system is numerically modeled on the FPGA by using the RK4 algorithm to generate a Chua's oscillator, and the Chua's oscillator generates a chaotic signal through the RK4 algorithm.

[0067] The control unit is electrically connected with the Chua oscillator, and the control unit is a Moore state machine, which is responsible for managing and scheduling different operations and functions of the Chua oscillator.

[0068] The analog converter is connected with the control unit for converting...

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Abstract

The invention discloses an improved Chua's system and an FPGA-based Chua's chaotic signal generator thereof, and provides an improved Chua's system which uses a composite hyperbolic tangent cubic nonlinear function, can generate a three-scroll chaotic attractor, and generates a three-scroll chaotic signal through a bifurcation diagram, a Lyapunov exponent, a phase diagram and a time domain diagram. The numerical value shows richer dynamic behaviors such as coexistence of multiple attractors, transient period, intermittent chaos, attractor offset and the like; and after constant excitation is added, the symmetric characteristic of the chaotic attractor is destroyed by the constant excitation. Compared with an existing Chua's system which generates multi-scroll Chua's chaotic signals by setting up an analog circuit, the invention provides an FPGA-based implementation mode of the improved Chua's system, so that the influence of factors such as temperature and component aging on result errors of a traditional Chua's analog circuit does not need to be considered.

Description

technical field [0001] The invention relates to the technical field of Chua's system, in particular to an improved Chua's system and its FPGA-based Chua's chaotic signal generator. Background technique [0002] In recent years, chaotic dynamics has become a very rich and widely used research field. Security communication, image encryption, memory, system synchronization, random number generator, complex network, etc. are all in-depth studies of chaos and its applications. [0003] Multi-scroll chaotic circuits have important applications in the fields of chaotic communication, information security and image encryption, and have become a hot spot in the research of chaos theory. To generate multi-scroll chaotic attractors in some simple chaotic systems, some nonlinear functions are needed, including piecewise linear functions, sawtooth waves, triangular waves, step waves, saturation functions, polynomial functions, trigonometric functions, and absolute value functions. Curr...

Claims

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Application Information

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IPC IPC(8): H04L9/00
CPCH04L9/001
Inventor 余飞沈辉张梓楠黄园媛蔡烁
Owner CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY
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