一类基于综合害虫管理策略的捕食系统的动力学性质

摘要

Based on the integrated pest management, a predator-prey system with impulsive effect is proposed and analyzed in this paper. By the Floquet theory and the comparison theorem of impulsive differential equation, it is proved that there exists a globally stable pest-eradication periodic solution when the impulsive period is less than some critical value. The sufficient condition for the permanence of the system is established. Numerical simulations illustrate the effect of impulsive on the dynamics of the system and the availability of our impulsive control strategy.%本文基于综合害虫管理策略,研究了一类具有脉冲效应的捕食模型并对其动力学性质进行了分析.根据Floquet乘子理论和脉冲微分方程的比较定理,证明了当脉冲周期小于某个临界值时,系统存在一个全局渐近稳定的害虫根除周期解,给出了系统持续生存的充分条件.数值分析进一步说明了系统的动力学性质及综合害虫管理策略的有效性.