一个类Lorenz系统若干动力学行为分析  

Analysis of Some Dynamics Behaviors Insight into a Class-Like Lorenz System

作　　者：邓奎彪[1] 韦小波[1] 赵启飞[1] 赵娟[1] 

机构地区：[1]柳州职业技术学院电子信息工程系,广西柳州545006

出　　处：《南通大学学报（自然科学版）》2015年第4期11-16,共6页Journal of Nantong University(Natural Science Edition)　

基　　金：广西教育厅自然科学基金项目(KY2015YB399)

摘　　要：研究了一个类Lorenz系统的若干动力学性质.利用中心流形定理分析了双曲平衡点和非双曲平衡点的稳定性.运用反证法证明了系统在平面中不存在闭轨,闭轨只能存在于空间中.通过分析说明在系统参数和初始值选择合适的条件下,存在退化奇异异宿环.最后,通过数值仿真验证了理论推导的正确性.The present work attempted to probte into some dynamical entities of a Lorenz-like chaotic system. The stability of hyperbolic equilibria, and the nonhyperbolic equilibrium were obtained by using the center manifold theo- rem. Using rebuttals of evidence, all the closed orbits of the system were proven rigorously to be nonplanar hut only to be curves in space. The existence of singularly degenerate heteroclinic cycles for a suitable choice of the parameters and initial conditions was analyzed. Finally, the theoretical assumption was confirmed through numerical simulation.

关 键 词：类LORENZ系统 动力学 中心流形定理 闭轨 奇异退化异宿环 

分 类 号：O415.5[理学—理论物理]