多滞量的反应扩散方程的分支环（I）──谨以此文庆贺肖伊莘先生八十大寿

Bifurcation of Tori in a Reaction-Diffusion Equation with Multiple Time Lage

本文研究一类定义在单位圆周上带有两个时滞的纯量反应扩散方程，在一定条件下，我们证明了方程在其平凡解处的线性化有一对简单的纯虚特征值±ｉω１，和一对重的纯虚特征值±ｉω２，且是非共振的（即ω１／ω１是无理数），然后，应用文［３］的中心流形的方法得到了一个六维常微分方程，用它来刻划方程在其平凡解邻域内的解的渐近性态。

In this paper,we study a class of scalar reaction-diffusion equations withtwo discrete time lags defined on the unit circle. Under certain conditions,we will showthat the linearization of the system at the trivial solution has a pair of purely imaginarysimple eigenvalues±iω1, a pair of purely imaginary double eigenvalues ± iω2 and themode is non-resonant(i.e.,ω1/ω2 is irrational).Using the technique of center manifoldreduction developed in Lin, So and Wu[3],we will obtain a 6-dimensional ordinary dif-ferential equation to characterize the asymptotic behaviors of the solutions to the abovesystem in a neighborbood of the trivial solution.