具有4个正Lyapunov指数的六维超混沌系统的复杂动力学研究  

Complex Dynamics of a Six-dimensional Hyperchaotic System with Four Positive Lyapunov Exponents

作　　者：邵慧婷 杨启贵[1] SHAO Huiting;YANG Qigui(School of Mathematics,South China University of Technology,Guangzhou Guangdong 510640,China)

机构地区：[1]华南理工大学数学学院,广东广州510640

出　　处：《广西师范大学学报（自然科学版）》2022年第5期433-444,共12页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(12071151);广东省自然科学基金(2021A1515010052)。

摘　　要：基于Lorenz系统,运用耦合技术和线性反馈控制,本文在仅有一个双曲平衡点的情况下发现一类新的具有4个正Lyapunov指数的超混沌吸引子的六维系统,且此系统在无穷多平衡点直线情形下具有3个正Lyapunov指数的超混沌吸引子。利用Routh-Hurwitz准则分析该系统双曲平衡点的稳定性,并证明该系统Hopf分岔的存在性。进一步运用相图、Lyapunov指数谱、Poincaré映射图及分岔图等计算机仿真技术,数值分析六维系统从周期、拟周期、混沌到超混沌等复杂动力学的演化过程。Based on the Lorenz system,a new six-dimensional hyperchaotic system with four positive Lyapunov exponents is found with only one hyperbolic equilibrium point by using coupling techniques and linear feedback control in this paper.Meanwhile,the system has three positive Lyapunov exponents for infinitely many equilibrium lines.The stability of the hyperbolic equilibrium point is analyzed by using Routh-Hurwitz criterion,and the existence of Hopf bifurcation is proved.Using computer simulation techniques such as phase diagram,Lyapunov exponential spectrum,Poincarémap,and bifurcation diagram,the complex dynamic evolution process of the six-dimensional hyperchaotic system from periodic,quasi-periodic,chaotic to hyperchaotic is analyzed numerically.

关 键 词：六维超混沌系统 吸引子 HOPF分岔 复杂动力学 稳定性 

分 类 号：O175[理学—数学]