Dynamics Of Stochastic Gilpin-Ayala Population Model With Impulsive Perturbations

In this thesis,based on the classical Logistic model,considering that the system is often affected by random perturbations,it also takes into account state switching between two or more environment,the dynamics of a stochastic Gilpin-Ayala population model with Markov switching and impulsive perturbations are established.Applying generalized ^ formula,quadratic variation,strong law of large numbers for martingales,ergodicity theory,and then construct a special Lyapunov function,the Gilpin-Ayala system is studied in depth.The existence,boundedness,extinction,non-persistence,weak persistence and stochastic persistence are obtained,it enriched the stochastic Gilpin-Ayala system with impulsive perturbations.In the first part of the thesis,the dynamic behavior of stochastic predation model with Gilpin-Ayala growth is studied,the Gilpin-Ayala parameter is also allowed to switch.By constructing the Lyapunov function,according to the properties of solutions of Logistic model,the existence of global positive solutions of the model is obtained.Applying generalized ^ formula,strong law of large numbers and ergodicity theory,sufficient conditions and the critical number for extinction,nonpersistence in the mean,weak persistence,and stochastic permanence are provided.The results show that the dynamic behavior of the model is closely influenced by the impulsive perturbations and Markovian switching.In the second part of the paper,The dynamic behavior of random predatorprey model with Gilpin-Ayala growth is investigated,the existence and uniqueness of global positive solutions has been proved.The sufficient conditions for extinction and persistence is obtained.Futhermore,the threhold value in the mean which governs the stochastic persistence and the extinction of the prey-predator system is obtained.The extinction of one population and the persistence of the other,the simultaneous extinction and coexistence of two populations also be discussed.