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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 43 ›› Issue (2): 287-300.doi: 10.3969/j.issn.1005-3085.2026.02.006cstr: 32411.14.cjem.CN61-1269/O1.2026.02.006

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新超混沌系统的动力学分析及其全局指数同步控制

张付臣1,  陈  松1,  陈修素1,  肖  敏2,3   

  1. 1. 重庆工商大学数学与统计学院，统计智能计算与监测重庆市重点实验室，重庆 400067

    2. 南京邮电大学自动化学院，南京 210023

    3. 南京邮电大学人工智能学院，南京 210023

  • 收稿日期:2023-09-21 接受日期:2024-04-18 出版日期:2026-04-15 发布日期:2026-06-15
  • 基金资助:
    国家自然科学基金 (62073172; 12371137)；江苏省自然科学基金 (BK20221329)；重庆市科委面上项目 (CSTB2022NSCQ-MSX1548)；重庆市教委科学技术研究专项 (KJCX2020037)；重庆市教委科学技术研究项目 (KJQN202100813; KJQN201800818)；重庆市高等教育教学改革研究项目 (253156)；重庆工商大学研究生教育教学改革项目 (24YJG307).

Dynamical Characteristics and Global Exponential Synchronization of a New Hyperchaotic System

ZHANG Fuchen1,  CHEN Song1,  CHEN Xiusu1,  XIAO Min2,3   

  1. 1. Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067
    2. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210023
    3. College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023
  • Received:2023-09-21 Accepted:2024-04-18 Online:2026-04-15 Published:2026-06-15
  • Supported by:
    The National Natural Science Foundation of China (62073172; 12371137); the Natural Science Foundation of Jiangsu Province (BK20221329); the Natural Science Foundation of Chongqing (CSTB2022NSCQ-MSX1548); the Chongqing Education Commission Science and Technology Research Project (KJCX2020037);  the Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJQN202100813; KJQN201800818); the Higher Education Teaching Reform Research Project of Chongqing Municipality (253156); the graduate teaching reform research project of Chongqing Technology and Business University (24YJG307).

摘要：

为了探究非线性系统中的超混沌现象，在超混沌Tang系统的基础上构建了一个新型超混沌系统。根据混沌动力系统的Lyapunov稳定性理论、定性理论和分岔理论研究了新的超混沌系统的混沌动力学特性，包括耗散性、平衡点及其局部稳定性、部分参数变化时的Lyapunov指数谱和分岔图等。通过引进广义Lyapunov函数，从数学理论上证明了新超混沌系统存在全局指数吸引集。利用全局指数吸引集的结果证明了用线性反馈控制方法使两个超混沌Tang系统达到全局指数同步，随后也给出了利用非线性反馈控制达到全局指数同步的控制器设计方法。最后通过数值仿真，证实了两种反馈控制方法都能达到全局指数同步，并对比了两种控制方法的优点。

关键词: 超混沌系统, 稳定性, 全局吸引域, 分叉, 全局指数同步

Abstract:

In order to investigate the hyperchaos phenomena in nonlinear systems, a new hyperchaotic system based on the hyperchaotic Tang system is constructed. Based on the Lyapunov stability theory, qualitative theory and bifurcation theory, the dynamical characteristics of this new hyperchaotic systems are studied, including dissipation, equilibrium point and its local stability, Lyapunov exponential spectrum and bifurcation diagram of some \mbox{parameters} change. By introducing the generalized Lyapunov function, it is proved that there exists the global exponential attractive set for the new hyperchaotic system. The global exponential synchronization of two hyperchaotic Tang systems is studied by using the global exponential attraction set and a linear controller is given to achieve global exponential synchronization. Then, a nonlinear feedback controller is presented to achieve global exponential synchronization. Finally, through numerical simulation, it is proved that both feedback control methods can achieve global exponential synchronization and the advantages of the two methods are compared.

Key words: hyperchaotic system, stability, global attraction domain, bifurcation, global exponential synchronization

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