Dynamical Properties Of Two Stochastic Leslie-gower Predator-prey Models

Predator-prey models have always been a hot kind of models studied in biomathematics.It is significant for ecology to study the conditions of survival and extinction of species.This paper considers a number of dynamical properties of two stochastic Leslie-Gower predator-prey models.In the introduction,the origin of Leslie-Gower predator-prey models as well as the study of deterministic and stochastic Leslie-Gower models are introduced.Lyapunov exponent is used to study those two models.A stochastic Leslie-Gower predator-prey model with Beddington-De Angelis functional response is studied in the second chapter.Firstly,Lyapunov exponents of ergodic invariant measures on the positive invariant sets are used to analyze stability of all boundary ergodic invariant measures.Secondly,using the stability of boundary ergodic invariant measures,the stability of all boundary invariant measures and inner invariant measures are obtained.Thirdly,by analyzing the stability of invariant measures,the survival and extinction thresholds of every species and stochastic dynamical bifurcations are obtained.Meanwhile,biological significances of stochastic dynamical bifurcations of models are also given.In the end,for all theoretical results,numerical simulation is used to verify them.In the third chapter,a stochastic Leslie-Gower food chain model with Holling-II functional response is studied by the same method in the second chapter.For three-dimensional model,however,two-dimensional ergodic invariant measures occur,which means it is more complicated than two-dimensional model.