Stability And Permanence Of A Periodic Populution Model With Impulsive Effects Over Patchy Environments

In the ecological environment,population dispersal and migration are a very common phenomenon.In our real life,the number of population is affected by the weather,season and other factors,so it is more practical to consider the population model in the periodic environment.In addition,population dynamic described by impulsive differential equations become a new hot topic of research.In this paper,we consider the single and m-patch population model with impulsive effects in a periodic environment.Furthermore,some sufficient conditions ensuring the stability and permanence of the pest-eradication periodic solution are detain.This paper has two main parts as follows:In first part of this paper,we study the population model with impulsive effects in a periodic environment,in which we consider some factors such as impulsively harvesting crop,spraying pesticide and releasing natural enemies at unfixed moments.Using impulsive comparison theorem,the linearization method and Floquet theory,we obtain some sufficient conditions on the locally and globally asymptotical stability of pest-eradication periodic solution.In the second part of the paper,we study the plant-pest-natural model with impulsive effects in patchy and periodic environment.On the basis of model in first part,we extend single patch model to m-patch model by considering the population diffusion,and consider some factors such as impulsively harvesting crop,spraying pesticide and releasing natural enemies at unfixed moments.By using the impulsive-type comparison theorem,linearization method and Floquet theory,sufficient conditions ensuring the globally asymptotical stability pest-eradication periodic solution are obtained.Furthermore,the permanence of the system is obtained by the persistence theory.Finally,two examples with m = 2 are given to verify the conclusion.