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3D unbalanced conservative chaos self-adaptive synchronous controller system with multistability

A chaotic system, multi-stable technology, applied in transmission systems, digital transmission systems, secure communication through chaotic signals, etc., can solve problems such as complex dynamic behavior of conservative systems, and achieve high security.

Inactive Publication Date: 2021-08-03
SHENYANG INSTITUTE OF CHEMICAL TECHNOLOGY
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  • Abstract
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  • Application Information

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Problems solved by technology

Then, the dynamic behavior of conservative systems with multi-stability is more complex and worthy of further study

Method used

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  • 3D unbalanced conservative chaos self-adaptive synchronous controller system with multistability
  • 3D unbalanced conservative chaos self-adaptive synchronous controller system with multistability
  • 3D unbalanced conservative chaos self-adaptive synchronous controller system with multistability

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Embodiment Construction

[0057] The present invention will be described in detail below in conjunction with the embodiments shown in the accompanying drawings.

[0058] 1 Nosé-Hoover conservative chaotic system is (17):

[0059] (17)

[0060] in, is a state variable. The Lyapunov exponent of system (17) is . It can be seen that the sum of the Lyapunov exponents of the system (17) is zero and the maximum Lyapunov exponent is positive 0.014. Therefore, system (17) is a conservative chaotic system. figure 1 The phase locus diagram of the system (17) is shown.

[0061] 2 Analysis of 3D conservative system

[0062] 2.1 Analysis of 3D dynamic model

[0063] Based on the conservative chaotic system (17), on this basis, the sinusoidal term and Adding two terms to the second equation yields a multistable 3D non-equilibrium conservative chaotic system:

[0064] (18)

[0065] In the formula, is a state variable, is a constant of the system, when When , the system (18) is a conservative...

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Abstract

The invention discloses a 3D unbalanced conservative chaos self-adaptive synchronous controller system with multistability, and relates to a self-adaptive synchronous controller system. The invention designs a self-adaptive controller system, realizes synchronous control of the system, and verifies effectiveness of the method by using theoretical analysis and numerical simulation results; and a phase diagram, a Lyapunov index, a balance point, a symmetry and the like indicate the chaotic characteristic and the complex dynamic behavior of the system, the bifurcation diagram analysis discovers that the system can generate different hidden chaos coexistence attractors in the same phase space along with the difference of initial conditions, and the multistability of the system is verified. Due to the fact that few literatures about a multistable conservative chaotic system exist, the system enriches the types of the conservative chaotic system, and meanwhile the multistable conservative chaotic system has important application value in the field of synchronous communication and digital image encryption.

Description

technical field [0001] The invention relates to an adaptive synchronous controller system, in particular to a multi-stable 3D non-equilibrium conservative chaos adaptive synchronous controller system. Background technique [0002] Chaotic systems have been extensively studied since Lorenz discovered the three-dimensional chaotic system model in 1963. These studies have laid the foundation for the application of chaos theory in engineering and scientific fields such as biology, information encryption, signal processing, and memristor. Most of these applications are studied based on chaotic dissipative systems. In the chaos literature, there are very few studies on conservative systems. People are very interested in its discovery. Classical conservative chaos includes Sportt-A system, Hénon-Heiles system, Nosé-Hoover system, etc. It is not difficult to find that these conservative systems are not multi-stable. Most of the studies on multi-stable states focus on dissipativ...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L9/00
CPCH04L9/001
Inventor 颜闽秀谢俊红
Owner SHENYANG INSTITUTE OF CHEMICAL TECHNOLOGY
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