三维离散类Lorenz系统的Neimark-sacker分岔  

An analysis of Neimark-sacker bifurcation for a new three-dimensional discrete Lorenz-like system

作　　者：杜文举[1,2] 张建刚[2] 俞建宁[1] 安新磊[2] 

机构地区：[1]兰州交通大学交通运输学院,兰州730070 [2]兰州交通大学数理学院,兰州730070

出　　处：《四川大学学报（自然科学版）》2015年第6期1297-1302,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(61364001;11161027);教育部科技研究重点项目(212180)

摘　　要：应用欧拉差分方法,构造了一个新的三维离散类Lorenz系统.讨论了该三维离散动力系统的动力学性质,分析了其不动点的存在性和稳定性.基于Neimark-Sacker分岔准则、中心流形定理和范式理论,研究了该系统Neimark-Sacker分岔的存在性、稳定性和方向.最后,通过数值仿真证明理论分析的正确性.A new three-dimensional discrete Lorenz-like system is proposed by using forward Euler scheme. The dynamics of this three-dimensional discrete Lorenz-like system is considered, and the existence and stability of equilibrium are also discussed. Based on explicit Neimark-Sacker bifurcation criterion, center manifold theory and normal form method, the system＇s existence, stability and direction of Neimark-Sacker bifurcation are studied. Finally, a numerical example is provided for justifying the valid- ity of the theoretical analysis.

关 键 词：离散类Lorenz系统 稳定性 中心流形定理 NEIMARK-SACKER分岔 

分 类 号：O193[理学—数学]