The Study Of Intermittent Dispersal Population Models With Stochastic Perturbations

The stochastic population ecology is a mathematical subject risen in recent years,there is extensive application on the stochastic mathematical biology. Owing to kinds of stochastic factors, species dispersal phenomenon in pathy environment will be affected. In addition, species dispersal phenomenon is neither successive nor instantaneous. Based on the research of predecessors, the stochastic mathematical biology is applied to population model by us in this paper. The parameters of determinative models can be randomized and we consider that species dispersal behaviors are intermittent, we make extensive study for the following dispersal models with white noise perturbations, including Single-species intermittent dispersal model with random perturbations between two and n patches, a predator-prey model with prey intermittent dispersal and random perturbations.In this paper, main contents can be summarized as follows four parts.In section 1, first of all, we introduce the ecological background of our research.Secondly, some current species' research situation and outcome are introduced by us.Once again, we introduce the main research contents.In section 2, we come up with a Single-species intermittent dispersal model with random perturbations between two and n patches. By constructing appreciate Lyapunov functions, applying for the Ito's formula, Gronwall inequality and Cheyshev's inequality of stochastic differential equation, some conditions on the global existence and uniqueness of a positive solution, ultimate boundedness in mean, stochastic permanence, and extinction in mean are established. Eventually, numerical simulations are given to confirm the validity of the theoretical results.In section 3, we propose a predator-prey model with prey intermittent dispersal and random perturbations. By constructing suitable Lyapunov functions, making use of the Ito's formula and available analysis methods, almost sufficient and necessary conditions are obtained for the existence of at least one strictly positive solution, stochastic permanence and extinction. Finally, using Matlab soft to make numerical simulations, our results are verified.In section 4, A summary is made by us.