一类混沌系统动力学行为的突变分析

Catastrophe Analysis of Dynamic Behaviour for A Chaotic System

通过对一类混沌系统突变行为的分析发现,在其突变区域,系统可出现2个由稳定不动点决定的混沌吸引子.随着系统参数的变化,当某个吸引子的吸引域逾越不稳定不动点界限或临界状态时,系统将突变到另一吸引子上,并且在系统参数变化范围相同的区域,若系统参数变化的趋势不同,系统的动力学行为不同.在突变区域,通过适当选取系统的初始值,可改变系统的动力学行为走向.

Through the analysis of catastrophe phenomena of a chaotic system,two attractors in the catastrophe region which are determined by two stable fixed points are found.When the domain of attraction of one attractor is beyond the unstable fixed point＇s boundary or the supercritical domain,the system will jump to the orbit of another attractor with the system parameters＇ changing.In the region,the dynamic behaviour of the system varies with the different changing trend of the system parameter,and the behaviour can be controlled by the reasonable choice of the original values.