一个微分生态系统的脉冲控制分析

Impulsive control analysis of differential ecosystem

在已有的功能性反应生态系统的基础上,研究了一个具功能性反应的微分生态系统的稳定性。应用脉冲微分方程的比较原理,对该微分生态系统进行脉冲控制,得出了系统平衡点渐近稳定的充分条件,给出了脉冲控制时间间隔的估计。采用数值举例方法说明了结论的有效性,并给出生态解释。结果表明,给定参数满足一定条件时两种群的密度可以保持一种稳定状态。

Based on ecosystem with functional response, the stability of a differential ecosystem with functional response is studied. The differential ecosystem is controlled impulsively by using comparison theorem ofimpulsive differential equations. The sufficient condition for the system’s equilibrium points to asymptotic stability is obtained. The upper bounds of the impulsive control time interval are estimated. The method is effective based on the example in number and the ecological explanation is given. It shows that the densities of preys and predators are stable if the given parameter satisfies certain conditions.