一类具有周期系数的脉冲种群模型稳定性分析

Stability Analysis of an Impulsively Population Control Model in Periodical Environment

摘要: 本文主要研究一类具有周期系数的脉冲种群控制模型的害虫灭绝周期解的稳定性问题。首先，建立在不同时刻收割庄稼、喷洒农药和释放天敌的一类具有周期系数的植物害虫天敌的脉冲控制模型。然后得到脉冲控制模型的两个害虫灭绝周期解，利用线性化方法、比较原理以及Floquet原理，分别给出害虫灭绝周期解局部稳定性和全局稳定性的一些充分条件。

Abstract: In the paper, we study the stability of pest-extinction periodic solutions of an impulsively popula-tion control model in periodical environment. First, we formulate a plant-pest-natural enemy model in periodical environment with harvesting, spraying and releasing at different moments. Then, we obtain pest-extinction periodic solutions. Some sufficient conditions for local stability and globally stability of pest-extinction periodic solutions are determined by the comparison technique of impulsive differential equations and the Floquet theory.