Five-dimensional hyper-chaotic system

A hyperchaotic and fifth technology, applied in the field of five-dimensional hyperchaotic systems, can solve the problems of complex circuit implementation and few hyperchaotic systems, and achieve the effect of large dynamic range and wide application value

Inactive Publication Date: 2013-12-11
王少夫
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  • Abstract
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  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0003] The disadvantage of the hyperchaotic system in the current technology is that the circuit is complex to realize, the system contains multiple equilibrium points, and there are few hyperchaotic systems with only three equilibrium points

Method used

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  • Five-dimensional hyper-chaotic system

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Embodiment Construction

[0036] The mathematical model of a five-dimensional hyperchaotic system of the present embodiment can be described as:

[0037] (1)

[0038] in , the five-dimensional chaotic system satisfies ( ) without deformation, with Axial symmetry;

[0039] make

[0040] (2)

[0041] It can be easily seen that the origin is an equilibrium point of the system ,when The other two equilibrium points are , .

[0042] at balance , the system (1) is linearized to obtain its Jacobian matrix as

[0043] (3)

[0044] for balance The corresponding eigenvalues, let

[0045] (4)

[0046] The corresponding eigenvalues ​​can be obtained The five eigenvalues ​​here are all real roots, but not all are negative real roots. According to the Routh-H...

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Abstract

The invention relates to a five-dimensional hyper-chaotic system. With introduction of two non-linear state feedback controllers, the novel five-dimensional hyper-chaotic system is put forward. A chaotic attractor can manifest a two-wing mode and a multi-wing mode in any directions. Because a large positive Lyapunov exponent exists, the chaotic system has complicated dynamics behaviors. Numerical simulation and analysis are performed on basic dynamics characteristics of the system, and discoveries are that the system has a constant Lyapunov exponent characteristic towards certain parameters. The system comprises a reverse proportion circuit, a first integrating circuit, a second integrating circuit, a third integrating circuit, a fourth integrating circuit and a fifth integrating circuit. Output ends of a first operational amplifier, a second operational amplifier, a third operational amplifier, a fourth operational amplifier and a fifth operational amplifier successively output x(x1), y(x2), z(x3), u(x4) and v(x5) which act as three state variables of the hyper-chaotic system. According to the simple five-dimensional hyper-chaotic system, the chaotic attractor of the simple five-dimensional hyper-chaotic system can manifest the two-wing mode or the multi-wing mode in any directions, and the simple five-dimensional hyper-chaotic system is simple in circuit realization so that the system only has three balance points, and has wide application prospects and important application value in the fields of radar, secret communication, electronic countermeasures, etc.

Description

technical field [0001] The invention relates to a five-dimensional hyperchaotic system. Background technique [0002] Ordinary signal sources can generate different periodic signals and have been applied in the field of information engineering, but it is not conducive to the requirements of special fields such as information encryption. Chaotic signals have the characteristics of inherent randomness, initial value sensitivity, broadband, ergodicity, and boundedness, and can generate broadband signals similar to white noise. Therefore, chaotic signals have broad application prospects in secure communication and other fields. Since Lorenz discovered the first mathematical model of chaos in 1963, the research on chaos in the nonlinear field has made great progress. Chaos has been widely used in secure communication. For the encrypted signal of a chaotic system signal with only one positive Lyapunov exponent, its secret signal is relatively easy to be deciphered, while the nat...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L9/00
Inventor 不公告发明人
Owner 王少夫
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