一类二维环境污染时滞微分方程动力学模型及其稳定性分析

A Class of Two Dimensional Dynamic Model with Time Delays Describing Environment Pollution and Its Stability Analysis

研究了一类环境污染相关的二维时滞微分方程动力学模型平衡点的稳定性与Hopf分支周期解的存在性,利用LaSalle不变性原理证明变界平衡点E_0在条件n-m≥a时是全局渐近稳定的;同时,给出正平衡点产生Hopf分支的充分条件。最后,数值模拟验证了理论结果。

In this paper, a class of two dimensional dynamic model with time delays describing environment pollution is proposed. The stability of equilibriums and existence of periodic solutions of a Hopf bifurcation are studied. Using the LaSalle invariance principle proved effective balance Eo in conditions of n-m≥a is global asymptotic stability. Then,the condition for the existence of Hopf bifurcation near the positive equilibrium were given. Finally, numerical simulations verified the theoretical results.