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Mathematical model of four-order complex-valued hyperchaotic system and implementation circuit

A mathematical model and ultra-chaotic technology, applied in the mathematical model of the fourth-order complex-valued hyper-chaotic system and the realization of the circuit field, can solve the problems of phase space reconstruction difficulties, etc., to achieve rich dynamic behavior, simple implementation, and easy integration Effect

Active Publication Date: 2020-09-04
ZHENGZHOU UNIVERSITY OF LIGHT INDUSTRY
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Problems solved by technology

In addition, compared with the low-dimensional chaotic system, the output sequence of the hyperchaotic system has multiple positive Lyapunov exponents, and its phase space is more difficult to reconstruct

Method used

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  • Mathematical model of four-order complex-valued hyperchaotic system and implementation circuit
  • Mathematical model of four-order complex-valued hyperchaotic system and implementation circuit
  • Mathematical model of four-order complex-valued hyperchaotic system and implementation circuit

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Embodiment Construction

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

[0041] The invention provides a mathematical model of a fourth-order complex-valued hyperchaotic system as:

[0042]

[0043] Among them, x, y, z, w are system state complex variables, a, b, c, d, r, e are system parameters; Both represent the derivatives of complex variables of the system state with respect to time.

[0044] let x=x 1 +jx 2 , y=x 3 +jx 4 , z=x 5 +jx 6 , w=x 7 , separate the real part and imaginary part of the complex variable in...

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Abstract

The invention provides a mathematical model of a four-order complex-valued hyperchaotic system and an implementation circuit, the mathematical model is composed of four nonlinear differential equations, and each differential equation comprises one nonlinear product term; the complex-valued hyper-chaotic system constructed by the mathematical model has three positive Lyapunov indexes and has very rich chaotic dynamics behaviors. The implementation circuit is characterized in that 23 operational amplifiers, 6 multipliers, 54 resistors and 7 capacitors form seven channel circuits, and 6 analog multipliers are used for achieving four quadratic product terms in a complex valued system; 23 operational amplifiers, 54 resistors and 7 capacitors are respectively used for completing addition, subtraction, voltage inversion and integration functions. The implementation circuit is simple to implement and convenient to integrate, and lays a foundation for application of the complex-valued hyper-chaotic system in the fields of information science, secret communication and the like.

Description

technical field [0001] The invention relates to the technical field of secure communication, in particular to a mathematical model and a realization circuit of a fourth-order complex-valued hyperchaotic system. Background technique [0002] Chaos refers to the uncertain or unpredictable random phenomenon presented by a certain nonlinear system under certain conditions, which embodies the relationship between certainty and uncertainty, order and disorder, or regularity and irregularity. Organic unity. Chaos' long-term unpredictability, ergodicity and extreme sensitivity to initial conditions indicate that chaos will be widely used in cryptography. [0003] The complex chaotic system is the generalization and extension of the research domain of the chaotic system from the domain of real numbers to the domain of complex numbers. It has an extremely deep background in physical research and plays an important role in the field of physics. There are complex variables in the comp...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06N7/08
CPCG06N7/08
Inventor 刘娜刘鹏李宗翰邓玮方洁栗三一孙军伟王国印
Owner ZHENGZHOU UNIVERSITY OF LIGHT INDUSTRY
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