摘要
提出一种新的类Lorenz系统,它具有三维二次型的自治常微分方程组形式.理论分析中,应用Lyapunov判定方法研究了系统平衡点的稳定性.在此基础之上,数值仿真表明,文中所考查的动力学系统具有极其丰富的动力学现象,包括混沌和多种形式的周期运动形式.文中还分析了两个重要参数对系统稳定性的影响,并通过构建一个受控系统分析了系统混沌吸引子的形成机制.
This article introduced a new Lorenz-like system of three-dimensional quadratic autonomous ordinary differential equations. For theoretical analysis, the Lyapunov criterion was applied to study the stability of the equalibria of the system. Based on this, numerical simulations indicated that the considered system may display abundant dynamical behaviour, such as chaotic and various periodic motions. Moreover, the effect of two key parameters on the stability of the system was investigated, and the forming mechanism of the chaotic attractor was studied via constructing a controller of the system.
出处
《动力学与控制学报》
2005年第4期1-6,共6页
Journal of Dynamics and Control
关键词
类LORENZ系统
混沌
形成机制
稳定性
Lorenz-like system, chaotic motion, forming mechanism, stability
