Asymptotic Behaviors Of Stochastic Hybrid Mutualism System With Lévy Jumps

In recent years,the population models with white noise random perturbation have been widely studied by scholars at home and abroad,and many important research results have been obtained.However,in the actual natural environment,there are other random noises,some of which may cause the system to have random regime switching,and some of which may cause the population number to change dramatically in a short time.In this paper,we study the asymptotic behavior of two kinds of stochastic hybrid population dynamical systems with Markov switching and Lévy jumps.The main contents are as follows:1.The asymptotic behavior of stochastic hybrid Gopalsamy mutualism model with Lévy jumps.By constructing appropriate Lyapunov function,we have prove the global existence and uniqueness of the positive solution of the model.On this basis,we discuss the ultimate boundedness of the model,and the sufficient conditions for the stochastic persistence of the model are given.We also prove the existence and uniqueness of the invariant distribution of the model without Lévy jumps.Finally,numerical simulation is used to verify that the model has a good persistence when the parameters satisfy the condition of random persistence.2.The asymptotic behavior of stochastic hybrid Gravesa mutualism model with Lévy jumps.Using the relevant knowledge of stochastic differential equations,we discuss existence and uniqueness of the global positive solution,the stochastic persistence,and extinction and persistence in mean.Then,we obtain not only the sufficient conditions for the stochastic persistence of the model,but also the threshold values of strong persistence,weak persistence,non persistence and tendency to extinction in mean of the model.Studies show that Lévy jumps may contribute to population tending to extinction,which demonstrates that jump noise may suppress the persistence.