Dynamical Behaviors Of Some Stochastic Biological Population Models With Time Delays

Stochastic differential equations have been widely used in aerospace,environmental protection,economics,ecology and so on.The problem of natural resources and ecological environment is becoming increasingly prominent.And there are many uncertain factors in the real natural environment,Therefore,the sustainable development of ecosystem becomes an important research subject.In this paper,the dynamics of several stochastic population models with time delay are studied.The main research works are as follows:For single population models,a stochastic Logistic model with time delays,white noises,Lévy jumps and capture is studied.It is proved that there is a unique positive solution to the model,and the uniform boundedness of the p-order for solution is discussed.The sufficient conditions for the extinction and persistence of each population have been established.The distribution stability of the model is proved.By using ergodic method,we establish sufficient conditions for the existence of optimal harvesting strategy of population models,and get explicit expression of optimal acquisition effort and maximum sustained yield.Under some mild conditions,time delay has no effect on the maximum sustained yield.For the two-dimensional population models,a stochastic competitive model with time delays,white noises,Lévy jumps and capture is considered.The sufficient conditions for each population to extinct and to persistent are established.The distribution stability of the model is proved.The existence of optimal harvesting strategy for the population model is proved by using the ergodic method.The effects of white noises,time delays and Lévy noises on maximum sustained yield are analyzed respectively.For the three-dimensional population models,a stochastic food chain model with time delays,white noises,Lévy jumps and capture is investigated.The sufficient conditions for each population to extinct and to persistent is established.And we prove the existence of optimal harvesting strategy by using the ergodic method.The effects of time delays and Lévy noises on maximum sustained yield are analyzed respectively.