一类非线性系统分岔混沌拓扑结构与全局复杂性  

Study on bifurcation topological structure and global complicated character of a non-linear system

作　　者：尹小舟[1] 刘勇[2] 

机构地区：[1]连云港职业技术学院,江苏连云港222006 [2]盐城师范学院数学系,江苏盐城224009

出　　处：《辽宁工程技术大学学报（自然科学版）》2009年第4期683-685,共3页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(10602020)

摘　　要：为了分析非线性系统在临界点附近的动力学行为,基于稳定性理论,讨论了CHEN系统平衡点的稳定性、局部拓扑结构及其全局复杂性.当2c?a≤0时,系统唯一的平衡点P=(0,0,0)是渐近稳定的;当2c?a>0时,系统有三个平衡点P和P±,且P是不稳定而P±是稳定的.系统在2c?a=0时产生分岔,其稳定的结点分岔出一双曲鞍点和两个稳定的汇,这就是Pitchfork分岔,可见在2c?a≤0变化到2c?a≥0时,吸引集AP从单点集变成为连接P和P±的两异宿轨道的并.同时给出了参数平面上的转迁集,这些转迁集将参数平面划分为不同的区域,在各个不同的区域对应于不同的解.系统随着参数的变化,从平衡点分岔出周期解.In order to comprehend the dynamical behaviour around critical points in a nonlinear system, this paper investigates the dynamical behaviour of CHEN system, the stability of equilibrium point, the local topological structure and global complicated character based on the stability theory. When 2c-a≤0, the system has a unique equilibrium point P = （0,0,0）, which is asymptotically stabilized. When 2c - a 〉 0, the system has three equilibrium points P andP^±, among them P is unstable and P^± are stable. In particular, the system generates bifurcation when 2c-a = 0, and then the stable knot bifurcates a hyperbolic saddle point and stable convergence, which is so-called Pitchfork bifurcation. From 2c - a 〈 0 to 2c - a 〉 0, the attracting set Ap of the system is changed from single point to the union set of two different old orbits. In addition, the transition set of parameter plane is given. The transition set divides the parameter plane into different regions with different corresponding solutions. The periodic solution can be bifurcated from equilibrium point with the variation of parameters.

关 键 词：CHEN系统 分岔 拓扑结构 全局复杂性 

分 类 号：O193[理学—数学]