一类延时系统的动力学行为研究

本文利用稳定性分析方法得到了一维延时系统定态稳定的充要条件。为研究系统的分岔和混沌行为,在长延时极限下对延时的倒数T_R^-1作渐近展开,得到的零级近似就是通常的一维映象,而T_R^-1的一级效应使系统运动的周期延长。更为有趣的现象是由更高级项带来的,T_R^-2项导致系统在每个分岔点出现滞迴过程(某种双稳现象);而T_R^-3项影响了系统的倍周期分岔行为:即分岔前后的周期之比并不是严格的二倍。高级效应还表明,在混沌带的合并点存在着不稳定窗口,并由此带来一些锁模现象。 关键词：

DYNAMICAL BEHAVIOR OF A SYSTEM WITH DELAYED FEEDBACK

In this paper, the necessary and sufficient conditions of a system with delayed feedback have been derived. In order to study the bifurcation and chaotic behavior, an asymptotic expansion of the solution in terms of the inverse delay time (T_R^-1) has been obtained. In long delay time limit, the first order effect in T_R^-1 is to prolong period of the motion. More interesting phenomena are about the higher order terms. The T_R^-2 terms lead to some hysteresis processes (some bistability) at each bifurcation point. And the third approximation in T_R^-1 influences the period-doubling bifurcation, i.e. the ratio of the periods below and at the transition point is not exact two. It is also shown that, some instable windows appear at merging points of the chaotic bands and lead to some mode-locked phenomena.