含两时滞捕食-被捕食系统的稳定性及分歧

本文研究一类含两相异时滞的捕食－被捕食系统的稳定性及分歧。首先，我们讨论两相异时滞对系统唯一正平衡点的稳定性的影响，通过对系数与时滞有关的特征方程的分析，建立了一种稳定性判别性。其次，将一个时滞看成分歧参数，而另一个看作固定参数，我们证明了该系统具有HOPF分歧特性。最后，我们讨论了分歧解的稳定性。

Stability and Bifurcation in a Predator Prey System with Two Delays

The purpose of this paper is to study the stability and Hopf bifurcation of a Lotka-Volterra system with two distinct delays.First,we investigate the effect of two distinct delays on stability on the unique positive equilibrium,by analyzing the corresponding characteristic equation with delay dependent coefficients;we give a kind of stability criterion involving the delays and the parameters.Second,taking one delay as a bifurcating parameter and another as a fixed parameter,we prove that the system exhibits the Hopf bifurcation.Finally,we study the stability of the bifurcating periodic solutions via the normal form theory.