一个新的三维类Lorenz系统的动力学分析及仿真  

Dynamics analysis of a new three-dimensional Lorenz-like system

作　　者：张旻[1] 张宇功 张建强[1] 

机构地区：[1]兰州交通大学数理学院,甘肃兰州730000

出　　处：《云南民族大学学报（自然科学版）》2015年第4期310-314,共5页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：甘肃省自然科学基金(1208RJZA111);甘肃省国际科技合作计划项目(1104WCGA195)

摘　　要：研究了一个新的三维自治类Lorenz系统,利用非线性动力学的相关理论分析了系统平衡点的稳定性以及Hopf分支,得到了系统发生Hopf分支时参数应满足的临界条件.通过数值仿真,分析了在多组参数下系统的各类动力学行为,进一步验证了理论推导的正确性.A three -dimensional continuous autonomous chaotic system is presented, which is similar to the Lorenz system. The non - linear dynamical method is used to study the dynamical behaviors of the Lorenz - like system, and some basic dynamical properties of the system are studied by means of theoretical analysis, numerical simulation, Lyapunov exponent, bifurcation diagrams, phase diagram, Poincare mapping; the complex dynamical behaviors of the chaotic system are analyzed with different system parameters, and the results show that the chaotic system has abundant dynamical behaviors.

关 键 词：LORENZ系统 混沌 LYAPUNOV指数 HOPF分岔 POINCARE截面 

分 类 号：O193[理学—数学]