The Study Of Impulsive Diffusion Patches Models With Markovian Switching

Species dispersal is one of the most ubiquitous prevalent phenomena in nature, The dynamic changes of all biological processes are a?ected by random ?uctuations. It is of great signi?cance to study the Random Impulsive di?usion model of the population.Many biological mathematics scholars have done a lot of research on this. On the basis of previous studies, We focus on the single population di?usion system and single population impulsive di?usion system. And in this paper, we studied a single species impulsive migration model with Markovian switching, a single species impulsive migration model with stochastic perturbation and probatilistic choice and single species symmetric dispersal model with random perturbation. We mainly get the exist of the global positivity of the solution of the system, and the ultimate boundedness, the random permanence, the extinction and so on.The main contents in this paper can be summarized as follows:In section 1, we introduce the ecological background of our study. Then, we introduce some current research situation and some research results about the di?usion model. We give the main research system ?nally.In section 2, we give the preparatory knowledge. In section 3, we give some de?nitions and some related lemma of this paper. And then, we give the system of a single species impulsive migration model with Markovian switching, In this system, the species of a patch can only choose a patch of patches in the impulsive time. Through analyzing and constructing appropriate Liapunov function, we establish the exist of the global positivity of the solution of the system, stochastic permanence, and the mean of the average extinction. Finally, numerical simulations are presented to illustrate our theoretical results.In section 4, we study the model of a single species impulsive migration with stochastic perturbation and probatilistic choice. And we give the further improvement of the third models is made, and in the impulsive time, Populations can di?usion between any number of patches. By constructing a suitable Liapunov function, using apagoge and Chebyshew inequality, we get there exist a global positive solution of the system, the stochastic Ultimate boundedness in mean and the extinction. Finally, numerical simulations are presented to illustrate our theoretical results.In section 5, we study the single species symmetric dispersal model with random perturbation, By constructing appropriate Liapunov function, we get the su?cient conditions on the global positive of the solution, the stochastic Ultimate boundedness in mean and pth moment exponential stability of the system.In section 6, we have a summary.