污染环境下具有脉冲输入环境毒素的单种群模型的灭绝阈值研究

本文研究了污染环境下具脉冲输入环境毒素的单种群模型.利用乘子理论和小振幅扰动法,当脉冲周期小于一个临界值时,我们得到了种群灭绝周期解是全局渐近稳定的,同时我们还得到了种群持久的条件.从生物学的观点看,污染环境下保护物种的方法是控制环境毒素的排放周期或排放量.我们的结论为资源环境下的生物资源管理提供了策略基础.

The Extinction Threshold on a Single Population Model with Pulse Input of Environmental Toxin in a Polluted Environment

We investigate a single population model with pulse input of environmental toxin in a polluted environment.By using Floquet theorem and small amplitude perturbation skills,we show that there exists a globally asymptotically stable population-extinction periodic solution when the period of impulsive effect is less than some critical value.The condition for the population's permanence is also given.From the biological point of view,it is easy to protect species by changing impulsive period of the exogenous input of toxicant,and toxicant input amount,etc.Our results provide tactic base for biological source management in a polluted environment.