一类微分差分方程周期解分支

THE Bifurcation of Periodic Solution for a Class of Differential Difference Equation

Kaplan-Yorke法是研究时滞微分差分方程周期解的重要方法之一.文中推广了该方法,结合分支方法研究了一类多时滞微分差分方程周期解的存在性和分支,给出了存在6k6+r1或6k6-r1周期解的新条件.特别研究了由五次多项式给出的微分差分方程在扰动下产生1个或多个周期解的问题,并获得了周期为6k6+r1或6k6-r1的小振幅分支周期解存在的一般条件.

Kaplan-Yorke＇s method is one of the important methods for studying the periodic solutions of delay differential equations. This paper developed this method and considered the existence and bifurcation of 6r/（6k＋1）（or6r/（6k-1））-periodic solutions for a class of delay differential equations. In partiular, it studied the equation with parameters and gave new conditions for the existence of periodic solutions. As an application, general conditions for the existence of one or more periodic solutions of delay differential equations defined by a polynomial with degree 5 were obtained.