The Study Of Population Models With Seasonal Succession And Markovian Switching

As the study of population ecology system is more and more deep,the influence of environmental changes on the population species has attached more attention.Many scholars and experts have done a lot of research on biomathematics population with environmental disturbances and obtained great achievement.However,the analytical conclusions and methods is not a lot so far.In this paper,by considering the effect the seasonal succession and impulsive perturbations imposed on population species,we establish “A single species model with seasonal succession and impulsive perturbations”and “Single-species model under seasonal succession alternating between Gompertz and Logistic growth and impulsive perturbations”,and “The stochastic interactions between predator and prey under Markovian switching: competitive interactions between members of a predator-prey model” based on stochastic disturbances.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 disturbance.Finally,we give the major work about our paper.2.In Section 2,we mainly discuss a class of single species with seasonal succession and impulsive perturbations.By establishing the stroboscopic map,the necessary conditions for the persistence and extinction of population are obtained,and combining the theory of rational difference equation and discrete dynamical systems,we obtain that the system has a unique globally stable positive periodic solution.The numerical simulation is taken by using mathematical software-Matlab,it clearly shows the influence of pulse disturbance and seasonal succession on species.3.In Section 3,a class of predator-prey model with prey competition is proposed,in which the interactions of predation between predator and prey are randomised and subsequently evaluated under Markovian switching.By constructing appropriate Lyapunov functions and applying various analytical methods,sufficient conditions for the existence of unique global positive solution,stochastic permanence and extinct in mean are established.Specific examples and numerical simulations are provided to demonstrate our theoretical results at last section.