一种具有共存吸引子的超混沌系统的动力学分析  

Dynamic analysis of a hyper-chaotic system with coexisting attractors

作　　者：李木子 许荣今 岳立娟[1] LI Mu-zi;XU Rong-jin;YUE Li-juan(School of Physics,Northeast Normal University,Changchun 130024)

机构地区：[1]东北师范大学物理学院,吉林长春130024

出　　处：《东北师大学报（自然科学版）》2021年第4期120-128,共9页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11947405);吉林省自然科学基金资助项目(20170101058JC).

摘　　要：提出了一个具有共存吸引子的新五维超混沌系统,系统无平衡点,因此具有隐藏吸引子.通过Lyapunov指数谱、分岔图、相轨迹图、Poincaré截面、参数盘等动力学分析,系统呈现出从周期、倍周期到混沌、超混沌的动力学行为,同时系统具有对称不变性.在参数不变仅改变初值的情况下,系统出现周期与超混沌吸引子共存、周期与混沌吸引子共存.该系统可以引入两个偏置,使吸引子能同时在两个方向上平移.通过参数盘的分析可见,在平移过程中吸引子类型发生了改变,而且具有超混沌与周期吸引子共存特性.改变初值和偏置两种情况均产生共存吸引子,进一步体现出该系统具有复杂的动力学特性.In this paper,a new five-dimensional hyperchaotic system with coexisting attractors is proposed.The system has no equilibrium points,so it has hidden attractors.Circuit simulation verifies the realizability of the system.Through dynamic analysis of Lyapunov exponential spectrum,bifurcation diagram,phase trajectory diagram,Poincarécross-section,parameter disk,etc.,the system exhibits dynamic behavior from period,period doubling to chaos and hyper-chaos.When the parameters are unchanged and only the initial value is changed,the system coexists with period and hyperchaotic attractors,and period and chaotic attractors coexist.Some interesting dynamics properties such as symmetric invariance and offset boosting are also presented.The system can introduce two constans so that the attractor can translate in both directions simultaneously.Through the analysis of the parameter disk,it can be seen that the attractor type has changed during the translation process,and it has the characteristics of hyper-chaos and periodic attractors coexistence.The coexistence attractors are generated by changing the initial value and offset boosting,which further reflects the complex dynamic characteristics of the system.

关 键 词：共存吸引子 偏置 新超混沌系统 

分 类 号：O415[理学—理论物理]