The Two Kinds Of Population Models With Discrete Intermittent Diffusion And Random Diffusion

In the real ecological environment,population diffusion is a very common phenomenon.The number of the population in a certain patch will fluctuate because of the influence of itself or external environmental factors.Population diffusion also affects the whole distribution and dynamic behavior of ecological species to a certain degree.Therefore,the population diffusion model has attracted the attention of many researchers.However,there are few articles about discrete intermittent diffusion and random diffusion.In this paper,by considering the effect the environmental conditions,we establish ”hybrid discrete population model with Beverton-Holt growth function and piecewise dispersal between two patches”,and ”single-species model with random dispersal between two patches”.The main contents can be summarized as follows:1.In Section 1,we first introduce the ecological background in this paper.Secondly,we give the current researches and results about population models with environmental disturbances.Finally,we give the major work about our paper.2.In Section 2,A class of Beverton-Holt growth-type two-patch hybrid discrete population model and intermittent predator-prey model are discussed in this paper.Both models are composed of two subsystems composed of difference equations: one subsystem diffuses between two patches,the other subsystem does not move between patches,and the population is in a habitat state.By using spectral radius theory and discrete dynamic system,the two subsystems are constructed.At the same time,the existence and boundedness of the two systems are given,and the threshold conditions for the extinction and persistence of the whole system are calculated.The bifurcation analysis of the neutron system is also carried out by using the bifurcation theory.Finally,the correctness of the theoretical analysis is verified by concrete examples and numerical simulation.3.In Section 3,a class of single-species model with random dispersal between two patches is proposed.The subsystem of model is composed of two parts: one part with dispersal between two patches,the other without movement between patches.By constructing appropriate Lyapunov function and applying various analytical methods,the existence of unique global positive solution,stochastic permanence and mean extinction are established.We conclude that population dispersal is not only dependent on subsystem coefficients,but also on the transition probability of Markov chain.Numerical simulations are provided to demonstrate our theoretical results.