一类超混沌Liu系统动力学分析  

Dynamics analysis in a hyperchaos Liu system

作　　者：张莉[1] 李耀伟[2] 俞建宁[2] 杨敏[2] 

机构地区：[1]兰州工业学院基础学科部,甘肃兰州730050 [2]兰州交通大学数理学院,甘肃兰州730070

出　　处：《山东理工大学学报（自然科学版）》2014年第6期14-19,24,共7页Journal of Shandong University of Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(61364001);甘肃省自然科学基金资助项目(1010RJZA067);教育部科技研究重点项目(212180);甘肃省高校科研业务基金资助项目(620023)

摘　　要：研究了一类四维超混沌Liu系统的基本动力学特性,求得了该系统的平衡点并分析了平衡点的稳定性,对平衡点进行了Hopf分岔分析,得出Hopf分岔的参数条件.运用范式的方法求得了系统发生Hopf分岔时极限环的方向和稳定性.对Liu系统进行的数值仿真结果验证了理论推导的正确性.A four-dimensional hyperchaos Liu system is proposed in this paper.Its basic dynamic characteristics are studied,the equilibria of the system is obtained through the simple calculation,then the stability of equilibria is analyzed.Through the analysis of Hopf bifurcation of equilibria,the parameter condition of Hopf bifurcation is derived.The stability and direction of limit cycle are derived by form theory.Simulation is given to illustrate the theoretical analysis with the aid of the computer.It is shown that the numerical results quite well with our theoretical analysis.

关 键 词：超混沌 HOPF分岔 平衡点 范式理论 数值仿真 

分 类 号：O415.5[理学—理论物理]