共存吸引子个数可调的混沌系统

doi:10.19596/j.cnki.1001-246x.8218

计算物理 ›› 2021, Vol. 38 ›› Issue (2): 244-252.DOI: 10.19596/j.cnki.1001-246x.8218

• 研究论文 • 上一篇

共存吸引子个数可调的混沌系统

颜闽秀^1,2, 徐辉¹

1. 沈阳化工大学信息工程学院, 辽宁沈阳 110142;
2. 工业环境-资源协同控制与优化技术辽宁省高校重点实验室, 辽宁沈阳 110142

收稿日期:2020-04-20 修回日期:2020-06-24 发布日期:2021-09-29
作者简介:颜闽秀(1972-),女,博士,副教授,主要研究方向为复杂系统控制和混沌理论,E-mail:cocoymx@sohu.com
基金资助:
国家科技部中国-马其顿政府间科技合作项目（国科外[2017]25：5-5）及辽宁省教育厅项目（LZ2016006）资助

A Chaotic System with Adjustable Number of Coexisting Attractors

YAN Minxiu^1,2, XU Hui¹

1. College of Information Engineering, Shenyang University of Chemical Technology, Shenyang, Liaoning 110142, China;
2. Key Laboratory for Industrial Environment-Resources Cooperative Control and Optimization Technology, Shenyang, Liaoning 110142, China

Received:2020-04-20 Revised:2020-06-24 Published:2021-09-29

摘要/Abstract

摘要： 运用Silnikov定理构建一个具有共存吸引子且个数可调的混沌系统。首先在经典混沌系统基础上构建一个结构简单的混沌系统，分析系统的动力学特性，验证系统马蹄意义下的混沌特性。在此基础上，将多零点分段函数引入该系统，以扩展系统平衡点的方式来增加系统的不变集，进而建立具有共存吸引子个数可调的混沌系统，由于共存吸引子的复杂性，该系统在保密通信领域具有较好的应用价值。

关键词: 混沌系统, 共存吸引子, 分段函数, 平衡点, Silnikov定理

Abstract: A chaotic system with adjustable number of coexisting attractors was proposed with Silnikov theorem. Firstly, a chaotic system with simple structure is constructed based on a classical chaotic system. Dynamic properties of the system are investigated and chaotic characteristics of the system in the sense of horseshoe are verified. Then, multi-zero piecewise function is introduced into the system to expand balance point of the system with adding invariant set of the system. A chaotic system with adjustable number of coexisting attractors is established. Due to complexity of coexisting attractors, the system has potential application in secure communication.

Key words: chaotic system, coexistence attractor, piecewise function, equilibrium point, Silnikov theorem

中图分类号:

O415.5

颜闽秀, 徐辉. 共存吸引子个数可调的混沌系统[J]. 计算物理, 2021, 38(2): 244-252.

YAN Minxiu, XU Hui. A Chaotic System with Adjustable Number of Coexisting Attractors[J]. Chinese Journal of Computational Physics, 2021, 38(2): 244-252.

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共存吸引子个数可调的混沌系统

A Chaotic System with Adjustable Number of Coexisting Attractors

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