Dynamics Of Several Classes Of Three-species Models In Stochastic Environment

In recent decades,with the rapid development of industry and agriculture,human beings continued to expand the scope and range of exploitation in natural resources,which leads to the disruption of the ecological balance such that the human living environment has been being seriously threatened.Therefore,some environmentalist have been being plagued by the far-reaching significant issue how to qualitatively and quantitatively assess the threat to population's survival and make optimal strategy to reduce environmental and economic losses and this issue has received widespread attention from scholars.Based on the background of population survival and the work done by previous generations,we establish several types of random three-group models.The main results are as follows:The first chapter introduces the origin and current situation of population ecology,and describes the development of white noise,Lévy noise and so on,and gives a brief introduction on the main work of this thesis.In the second chapter,we list the definitions and lemmas in this paper.In the third chapter,dynamics of stochastic three-species predator-prey model are studied in a polluted environment.We first show that the stochastic model has a globally unique equilibrium solution,and establish sufficient criteria for the extinction,non-persistence,weak persistence in the mean,strong persistence in the mean and globally attractive of each species in the model.Finally,we use simulation technology to verify the validity of the theoretical analysis.In the fourth chapter,stochastic three-species competitive model with Lévy noise is proposed and investigated.Under some simple assumptions,we establish sufficient conditions for the extinction or persistence in the mean of each population,and study the asymptotic stability of the solution in the model.Finally,numerical simulations are carried out to verify the theoretical results.In the fifth chapter,a stochastic Leslie-Gower Holling-type II two-predators one-prey model with Lévy noise is proposed and considered.Firstly,we study the existence and uniqueness of the equilibrium point of the model.At the same time,sufficient conditions forthe extinction and persistence of each population are established.Finally,numerical simulations are carried out to verify the theoretical results.