具有有限和无限孤立奇点的新四维超混沌系统的复杂动力学分析  

Research on Complex Dynamics of a New Four-dimensional Hyperchaotic System with Finite and Infinite Isolated Singularities

作　　者：阮文静 杨启贵[1] RUAN Wenjing;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）》2021年第5期173-181,共9页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(12071151)。

摘　　要：基于Sprott A混沌系统,通过设计反馈控制器,提出具有无限多个孤立奇点和仅2个对称奇点的新四维自治超混沌系统;运用中心流形理论探讨这类新系统非双曲奇点的稳定性,严格证明了Hopf分岔;进一步,利用Lyapunov指数谱、分岔图及Poincaré映射等数值方法,获得了新系统周期吸引子、混沌吸引子及超混沌吸引子的存在性。Based on the Sprott A chaotic system,by designing a feedback controller,this paper proposes a new four-dimensional autonomous hyperchaotic system with an infinite number of isolated singularities and only two symmetrical singularities.The stability of the non-hyperbolic singularities of this type of new system is discussed by using the central manifold theory,and the Hopf bifurcation is strictly proved.Furthermore,by using numerical methods such as Lyapunov exponential spectrum,bifurcation graph and Poincarémapping,the existence of periodic attractors,chaotic attractors and hyperchaotic attractors of the new system is obtained.

关 键 词：超混沌 吸引子 HOPF分岔 复杂动力学 稳定性 

分 类 号：O415.5[理学—理论物理]