新五维超混沌系统的动力学和自适应同步分析  

Dynamics and Adaptive Synchronization Analysis of New Five-dimensional Hyperchaotic Systems

作　　者：李瑞梅 周艳[1,2,3] 崔壮 LI Ruimei;ZHOU Yan;CUI Zhuang(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application,Hohhot 010022,China;Center for Applied Mathematical Science,Inner Mongolia Normal University,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022 [2]无穷维哈密顿系统及其算法应用教育部重点实验室,呼和浩特010022 [3]内蒙古师范大学应用数学中心,呼和浩特010022

出　　处：《内蒙古农业大学学报(自然科学版)》2025年第2期81-89,共9页Journal of Inner Mongolia Agricultural University(Natural Science Edition)

基　　金：国家自然科学基金项目(12462004);内蒙古师范大学数学一流拔尖培育学科建设资助项目(2024YLKY01);内蒙古师范大学高校基本科研业务费项目(2023JBBJ004);内蒙古自治区自然科学基金重点项目(2022ZD05)。

摘　　要：本文主要分析了一个新五维超混沌系统的动力学特性及自适应同步,从耗散性、Lyapunov指数图及平衡点的稳定性等方面考察其动力学特性,结合无源性理论及自适应控制的方法考虑了系统间一种基于无源性的自适应同步问题。最后,通过MATLAB进行数值模拟,绘制了状态变量和误差变量的时域波形图,结果显示系统间实现了自适应混合同步。数值模拟结果表明,同步理论分析的正确性及同步方法的有效性。The dynamical properties and adaptive synchronization of a new five-dimensional hyperchaotic system were analyzed.The dynamical properties were examined in terms of dissipativity,Lyapunov exponential diagram,and stability of the equilibrium point.A Passivity-based adaptive synchronization problem between the systems was considered by combining the theory of passivity and the adaptive control method.Finally,numerical simulations were carried out by using the MATLAB software.Time-domain waveform di-agrams of the state variables and error variables were plotted.The results showed that adaptive hybrid synchronization was achieved between the systems.The numerical simulation results demonstrated the correctness of the theoretical analysis of synchronization and the effectiveness of the synchronization method.

关 键 词：超混沌系统 自适应控制 无源性 自适应同步 

分 类 号：O193[理学—数学]