A Research On Dynamical Properties Of Several Population Systems

The dynamical properties of several population systems under different environmental conditions has been studied in this paper.It’s mainly grouped into the following three parts.The first part of the study is a predator-prey system with partial benefit relationship.The conditions of the existence of the equilibrium are given.By constructing some suitable Liapunov functions,we obtain the sufficient conditions of the global asymptotic stability of the positive equilibrium and boundary equilibrium.In the end,numerical simulations are carried out to illustrate the effectiveness of our main results.Secondly,a stochastic delay competition system driven by L′evy noise under Regime Switching is considered.Both the existence and uniqueness of the global positive solution are examined.By comparison theorem,sufficient conditions for extinction and non-persistence in the mean are obtained.Furthermore,we show that the global positive solution is stochastically ultimate boundedness under some conditions,and an important asymptotic property of system is given.In the end,numerical simulations are carried out to illustrate our main results.Thirdly,a pest management SI stochatic model with effect of pesticides function is proposed.By constructing comparison systems and using comparison theorem of stochatic differential equation,the existence and uniqueness of the global positive solution,the boundedness of expectation and the global attractivity of the system are all proved.The sufficient condition of non-persistence in the mean and extinction are established.In the end,we give the numerical simulations to illustrate the effectiveness of our main results.