广西师范大学学报（自然科学版） ›› 2023, Vol. 41 ›› Issue (6): 8-21.doi: 10.16088/j.issn.1001-6600.2023040201

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多维混沌系统的构建及其多通道自适应控制

颜闽秀*, 靳琪森   

  1. 沈阳化工大学 信息工程学院, 辽宁 沈阳 110142
  • 收稿日期:2023-04-02 修回日期:2023-05-01 发布日期:2023-12-04
  • 通讯作者: 颜闽秀(1972—), 女, 福建仙游人, 沈阳化工大学副教授, 博士。 E-mail: yanminxiu@syuct.edu.cn
  • 基金资助:
    中国—北马其顿政府间科技合作项目(国科外[2019]22: 6-8); 辽宁省教育厅基本科研项目(LJKMZ20220779); 辽宁省自然科学基金(2022-BS-211); 沈阳市科技计划项目(22-322-3-38)

Construction of Multi-dimensional Chaotic Systems and Its Multi-channel Adaptive Control

YAN Minxiu*, JIN Qisen   

  1. College of Information Engineering, Shenyang University of Chemical Technology, Shenyang Liaoning 110142, China
  • Received:2023-04-02 Revised:2023-05-01 Published:2023-12-04

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摘要： 为改善低维混沌系统行为简单、密钥空间小等问题,本文提出一种多维混沌系统的设计方法,给出了系统结构及其平衡点通式,利用Si’lnikov定理验证该系统具有Smale马蹄意义下的混沌性质。以三维混沌系统为例,对该混沌系统进行动力学特性分析及其偏移增强控制,并利用Multisim电路仿真软件搭建该混沌系统,验证了系统的可实现性。基于自适应理论,设计一种多通道的自适应同步控制器,能够实现多种系统误差组合下的同步,提高了混沌系统在保密通信中的安全性。

关键词: 混沌系统, Si’lnikov, 同宿轨道, Smale马蹄, 混沌电路, 同步控制

Abstract: To solve the problem of simple behavior and small key space in low dimensional chaotic systems, a design method of multi-dimensional chaotic systems is proposed. The general formula of system structure and equilibrium point are given, and the chaotic property of Smale horseshoe system is verified by Si’lnikov theorem. Taking a three-dimensional chaotic system as an example, its dynamic characteristics are analyzed and its displacement control is enhanced. The chaos system is constructed by Multisim circuit simulation software, and the realization of the system is verified. Based on the adaptive theory, a multi-channel adaptive synchronization controller is designed. The controller can realize synchronization under various system error combinations and improve the security of chaotic systems in secure communication.

Key words: chaotic system, Si’lnikov, homologous orbit, Smale horseshoe, chaotic circuit, synchronous control

中图分类号:  O415.5;TP273

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