With Beddington Functional Response Systems Research And Computer Simulation

Contrasting with some common ecological phenomena in ecology,the author constru- cted a series of complicated ecological models with Beddington type functional respon- se on the basis of the traditional predator-prey models, which makes the model accord with the reality further. And we mainly probed into the permanence, the existence of the positive periodic solution or the almost-periodic solution and the asymptotic behavior of the corresponding system in this thesis. Based on an impulsive differential equations'theory, we introduce dynamical models with Beddington type functional response and pulse. The various dynamical behavior of the population models are globally studied. We carefully analyze the complexity of the chaos behaviors of the given systems by using the international computer algebra system Maple.In Chapter 2, we consider a predator-prey system with Beddington type functional response in a patchy environment. By constructing suitable Lyapunov functional, we study the permanence of the system. By Brouwer's fixed point theory, if the system is periodic, the system at least exists a positive periodic solution in certain conditions. For the case of almost-periodic system, by of coincidence degree theory, we obtain the sufficient conditions that the system exists a unique positive periodic solution, which is globally asymptotic stable.Considering the coincidence of the diffusion and delay in the reality conditions, we probed into a non-autonomous Beddington type functional response predator-prey system with both diffusion and discrete delay. By constructing suitable Lyapunov functional, we study the permanence of the system. By Brouwer's fixed point theory, if the system is periodic, the system at least exists a positive periodic solution in certain conditions. For the case of almost-periodic system, with the help of coincidence degree theory, we obtain the sufficient conditions that the system exists a unique positive periodic solution, which is globally asymptotic stable.Impulsive dynamical system is possible one of the most young and most attracting fields in main mathematical branches such as differential equations, dynamical systems, control theories etc. The theory of impulsive differential equations is not only richer...