一类三维自治混沌系统的动力学行为分析  

Dynamical analysis of a Lorenz-like chaotic system

作　　者：刘熙娟[1] 陈多花 

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《贵州师范大学学报（自然科学版）》2015年第4期55-61,共7页Journal of Guizhou Normal University：Natural Sciences

基　　金：甘肃省国际科技合作计划项目(1104WCGA195);甘肃省自然科学基金资助项目(1208RJZA111);甘肃省教育厅硕导基金项目(No.212104)

摘　　要：理论分析了一个三维自治系统的动力学特性,并通过数值计算分析了系统在平衡点的稳定性,以及系统产生Hopf分岔的条件。通过数值模拟出系统的分岔图,Lyapunov指数图,Poincare截面图,具体分析系统的动力学行为。最后通过参数控制仿真出相图来观察这种新的混沌吸引子结构的形成过程。The dynamical characteristics of a new Loren-like chaotic system are analyzed in detail. The stability of the fixed point is studied by numerical computation,which gets the condition of producing Hopf bifurcation. Then through numerical simulation,we can get the system ＇s bifurcation diagram,Lyapunov exponent spectrum,Poincare map,by which we can analysis its dynamical behavior detailedly. At last,through observing the phase portraits,one can get the forming mechanism of this new chaotic attractor structure with the control of the parameters.

关 键 词：新类Lorenz系统 HOPF分岔 LYAPUNOV指数 平衡点的稳定性 

分 类 号：O322[理学—一般力学与力学基础]