一个类Lorenz系统的动力学分析  

Dynamics Analysis of a Lorenz-like System

作　　者：李群宏[1] 徐德贵[1] 

机构地区：[1]广西大学数学与信息科学学院

出　　处：《重庆理工大学学报（自然科学）》2011年第2期112-116,共5页Journal of Chongqing University of Technology：Natural Science

基　　金：广西自然科学基金资助项目(2010GXNSFA013110);广西青年科学基金资助项目(0832014)

摘　　要：针对新提出的三维自治连续时间类Lorenz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Lyapunov系数的分析,推导出系统发生余维二退化Hopf分岔的参数条件。借助计算机对类Lorenz系统进行数值仿真,得到该系统发生退化Hopf分岔的分岔图,与理论推导结果相符合,从而验证了理论推导的正确性。A three-dimensional autonomous continuous Lorenz-like system proposed newly is studied in this paper.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.Parameter conditions for the codimension-2 degenerate Hopf bifurcation are presented by analyzing the first Lyapunov coefficient of the above system.Bifurcation diagrams of the aforementioned system,which demonstrate the degenerate Hopf bifurcation,are obtained by numerical simulations with the aid of the computer.It is shown that the numerical results agree quite well with the analytical ones and it validates our theoretical analysis.

关 键 词：HOPF分岔 退化HOPF分岔 第一Lyapunov系数 数值仿真 

分 类 号：O175[理学—数学]