Dynamic Behaviors Of Several Kinds Of Ecosystem With Nonlinear Functional Response

This paper consists of three parts as follows:Firstly,a discrete competitive system with nonlinear inter-inhibition is proposed and studied.By using the Jacobian matrix analysis method,the local stability of the system is investigated.Using the interative method and the comparison principle of difference equation,some suffici.ent conditions which guarantee the global stability of the system are obtained.The method we used here could be applied to continuous system and some corresponding result could be established,the result supplement and complement the main results in[2].Some examples together with their numerical simulations are presented to verify the feasibility of our results.Secondly,a nonautonomous modified Lesile-Gower predator-prey model with nonmonotonic functional resopnse and a prey refuge is investigated.By using the differential inequalities,sufficient conditions which ensure the permanence of the system are obtained.Furthermore,we also obtain sufficient conditions which ensure the extinction of the prey species.By constructing a suitable Lyapunov function,we obtain sufficient conditions which ensure the global stability of the positive solution of the system.Our study shows that enough large prey refuge could lead to the coexistence of the two species and the refuge has positive effect to the stability property of the system.By constructing a suitable Lyapunov function and Theorem 6.3 in[33],sufficient conditions which guarantee the existence,uniqueness and the global attractivity of the almost periodic solution are obtained.Examples together with their numerical simulations show the feasibility of our results.Thirdly,we propose a single-species system with Holling-IV functional response and feedback control.By applying the comparison theorem of differential equation and constructing some suitable Lyapunov functional,sufficient conditions which ensure the permanence and the global stability property of the system are obtained.An example together with its numerical simulation shows the feasibility of our results.