The Study Of Population Dynamics Behavior With Impulsive Diffusion

Species dispersal and migration are one of the most prevalent phenomena in thenatural world, and therefore become one of the most interested subjects for researchersno matter in home and abroad. In this paper, based on the study of other authors, wegive a more depth and abroad research about the species dispersal and migration. Themain contents of this paper include: impulsive dispersal of plant seeds in weak patch anda predator-prey system with prey impulsive di?usion between two patches.The main contents in this paper can be summarized as follows:1. In section 1, firstly, we introduce the ecological background of this paper. Then,it is given that some research conclusion recently about continuous dispersal system andimpulsive dispersal system. We investigate our research system finally.2. In section 2, it is studied that impulsive dispersal of plant seeds in weak patch. Byusing comparison theory and some analysis methods, su?cient and necessary conditionsof integrable form for pests-extinction periodic solutions of global attractivity and thepermanence of the periodic system, respectively. Lastly, an example is given.3. In section 3, we study a predator-prey system with prey impulsive di?usion be-tween two patches, su?cient and necessary conditions of integrable form for predator-extinction periodic solutions of global attractivity and the permanence of the periodicsystem are established by applying some analysis methods and comparison theory. Lastly,an example is given.