一类非线性自治Liu系统的Hopf分岔分析  

Hopf bifurcation analysis in a nonlinear autonomic Liu system

作　　者：李耀伟[1] 张莉[2] 杨敏[1] 

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

出　　处：《云南民族大学学报（自然科学版）》2014年第2期119-123,共5页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(61364001);甘肃省自然科学基金(1010RJZA067)

摘　　要：针对新提出的三维自治Liu系统进行研究,求得该系统的平衡点,并分析平衡点的稳定性.对平衡点进行了Hopf分岔分析,得出Hopf分岔的参数条件.通过对系统的第一李雅普诺夫系数的分析,推导出系统发生超临界、亚临界以及余维二退化Hopf分岔的参数条件.对Liu系统进行数值仿真,验证了理论推导的正确性.A three-dimensional autonomous Liu system proposed recently is studied. The equilibrium of the system is obtained through the simple calculation, and then its stability is analyzed. Through the analysis of Hopf bifurcation of the equilibrium, the parameter condition of Hopf bifurcation is derived. Parameter conditions for the supercritical, the subcritical and the codimension two degenerating Hopf bifurcation are presented by analyzing Lyapunov＇ s first coefficient of the system. Numerical simulation is given to illustrate the theoretical analysis with the aid of the computer. It is shown that the numerical results agree quite well with our theoretical analysis.

关 键 词：HOPF分岔 POINCARÉ截面 第一李雅普诺夫指数 数值仿真 

分 类 号：O415.5[理学—理论物理]