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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台实际,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.本文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.
The results of the research on population dynamics system described by differential equations are very rich, but many changes in nature show the pulse effect, so the impulsive differential equation is used to describe the rapid change of some motion states at fixed or unfixed moment Or jumping more to cut the reality, especially in describing the population growth and epidemiological dynamics behavior, the description of impulsive differential equation appears to be more scientific and more realistic .Studies on the population dynamics model with impulsive effect is still in its infancy stage. In this paper, we study the model of periodic damage with a constant coefficient of periodic structure with impulsive effect, and obtain the sufficient conditions for the existence of periodic solutions of the system. The sufficient conditions for the existence of unique periodic solutions and the sufficient conditions for the asymptotic stability of the system to be asymptotically stable are obtained .