污染环境下具有时滞增长反应和脉冲输入的单种群模型分析

Dynamical Analysis of a Single Population Model with Delayed Growth Response and Pulse Input in Polluted Environment

研究污染环境下具有时滞增长反应和脉冲输入的单种群动力学模型,利用脉冲微分系统讨论营养基和毒素的脉冲输入对单种群物种生长的影响,证明微生物在吸收毒素的情况下灭绝的周期解是全局吸引的,并获得系统持久的条件.研究结果为控制环境中毒素对种群生长的影响提供了理论依据.

In this paper, a single population dynamic model with deplayed response in growth and pulse input in polluted environment is considered. Using impulsive differential system, we study the effect of pulse input of nutrient and toxicant on a the growth of single species. A microorganism-extinction periodic solution is obtained and furthermore it is globally attractive. The permanent condition of the system is obtained by the theory on impulsive differential equation. Our results provide theory basis for the control of toxicant influence on population growth.