具阶段结构害虫防治模型的脉冲效应

对于用微分方程描述的种群生态动力系统，其研究结果已十分丰富，但自然界中的许多变化规律都呈现出脉冲效应，因此用脉冲微分方程描述某些运动状态在固定或不固定时刻的快速变化或跳跃更切合实际，尤其在刻画种群生长和流行病动力学行为方面，脉冲微分方程的描述显得更科学更真实，具有脉冲效应的种群动力学模型的研究目前还处于刚刚起步阶段，本对符合实际的有脉冲效应的具阶段结构的常系数害早防治模型进行了研究，得到了系统存在周期解的充分条件，系统存在唯一周期解的充分条件，系统周期解轨道渐近稳定的充分条件。

Impulsive Control of a Stage-structured Pest Management System

Biological dynamical systems described by ordinary differential equations have been studied by many authors and the research results are very rich. But many phenomena exhibit impulsive effects, so it is more natural to describe the processes with impulsive differential equations. This is particularly ture in the case of describing the growth of species and the behavior of epidemic dynamics. A beginning is just made in the application of the theory of impulsive differential equations to ecological systems. In this paper, we consider a stage-structured pest management system with impulse effects and constant coefficients that is more correspond with natural phenomena. The sufficient conditions of the existence, uniqueness and orbitally asymptotic stability of periodic solution are obtained.