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Chaotic circuit with coexistent asymmetric multi-attractors

A chaotic circuit and attractor technology, applied in CAD circuit design, electrical digital data processing, special data processing applications, etc., to achieve the effect of simple structure

Inactive Publication Date: 2017-08-11
CHANGZHOU UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

Multi-stability and super-multi-stability provide great degrees of freedom for engineering applications of nonlinear dynamical systems, but also pose new challenges to multi-stable state switching control technology

Method used

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  • Chaotic circuit with coexistent asymmetric multi-attractors
  • Chaotic circuit with coexistent asymmetric multi-attractors
  • Chaotic circuit with coexistent asymmetric multi-attractors

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Embodiment Construction

[0023] A chaotic circuit with coexisting asymmetrical multi-attractors of the present invention contains two non-linear items described by absolute value functions, and is a third-order chaotic circuit with a degenerate Jerk form.

[0024] 1. System equation: the mathematical model of a kind of asymmetric three-dimensional chaotic system that the present invention proposes can be expressed as

[0025]

[0026] Among them, x, y, z are three state variables, a, b, c are three system parameters and are all normal numbers.

[0027] System (1) is asymmetric. But system (1) is dissipative, and its dissipative property can be derived from the following expression

[0028]

[0029] Therefore, system (1) is always dissipative, and as time continues to evolve, all system trajectories will eventually be limited to a set with zero volume, and its asymptotic motion is fixed on an attractor.

[0030] Let the left side of the equation of the system (1) be equal to zero, and the syste...

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Abstract

The invention discloses a chaotic circuit with coexistent asymmetric multi-attractors. The circuit contains two nonlinear terms described by an absolute value function and is a third-order chaotic circuit with a degraded Jerk form. The circuit is composed of a reversal, addition and integration operational module based on an operational amplifier and a resistor or a capacitor and a nonlinear operational module composed of an analog multiplier and an operational amplifier. Under a certain initial condition, the circuit can display a coexistent phenomenon, namely a multi-stability phenomenon of the asymmetric multi-attractors. As a result, a great degree of freedom is provided for engineering application of a nonlinear dynamic system, and meanwhile the circuit has important theoretical physical significance and engineering application value for research about realization of the coexistent multi-attractors and a hardware circuit comprising the coexistent multi-attractors.

Description

technical field [0001] The invention relates to an autonomous chaotic circuit, which can realize the coexistence of multiple stable states by changing the initial state when the system parameters are constant, and can be used as a multi-random chaotic signal source. Background technique [0002] Multiple stability, that is, coexistence of multiple attractors is a strange physical phenomenon often encountered in nonlinear dynamical systems. When the system parameters remain unchanged, the initial state is changed, and the system's operating trajectory may asymptotically tend to the point, chaos, and periodicity. , quasi-periodic and other stable states. In some special coupling systems and novel memristive circuits, the coexistence phenomenon of infinitely many attractors can also be observed, that is, super multiple stability. Common coexisting multi-attractors generally have symmetry, and there are symmetrical coexistence phenomena of left and right or up and down attracto...

Claims

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Application Information

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IPC IPC(8): G06F17/50
CPCG06F30/30G06F30/367
Inventor 包涵包伯成王宁陈墨武花干
Owner CHANGZHOU UNIV
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