一个周期性强迫的四维超混沌系统的复杂动力学性质  

COMPLEX DYNAMICAL PROPERTIES OF A FOUR-DIMENSION PERIODICALLY-FORCED HYPERCHAOTIC SYSTEM

作　　者：陈熙统 鲍江宏 Chen Xitong;Bao Jianghong(Institute of Mathematics,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]华南理工大学数学学院,广州510640

出　　处：《动力学与控制学报》2021年第4期8-15,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11671149)。

摘　　要：基于Hide-Skeldon-Acheson系统,构建了一个新的四维周期性强迫的超混沌系统,不仅包含三角函数非线性项和三次多项式,而且具有无穷多个孤立平衡点.首先分析了新系统的平衡点与稳定性;然后发现在适当的参数条件下,周期解和隐藏混沌吸引子共存的多稳定(multistability)性质.进一步研究表明系统具有可共存可数无穷多个周期解或混沌吸引子的大稳定(megastability)性质;最后研究了系统的Hopf分叉,数值模拟证实了理论的结果.Based on the Hide-Skeldon-Acheson system,a new four-dimension periodically-forced hyperchaotic system is constructed,which not only contains nonlinear terms of trigonometric function and cubic polynomial,but also has infinitely many isolated equilibria.Firstly,the equilibrium and stability of the new system are analyzed,and then a multistability property is found with appropriate parameters,i.e.,periodic solutions and a hidden chaotic attractor coexist.Further studies show that the current system has a megastability property,i.e.,countable infinite periodic solutions or chaotic attractors coexist.Finally,Hopf bifurcation of the system is studied,and numerical simulations verify the theoretical results.

关 键 词：超混沌 隐藏吸引子 多稳定性 大稳定性 HOPF分叉 

分 类 号：O415.5[理学—理论物理]