With Stage Structure Predator-prey Model And Space Simulation

In recent years,the research of population space dynamics has been a hot topic of ecological mathematical model research. Environmental carrying capacity is introduced into a class of predator-prey system with stage of prey in this paper. And we obtain the conditions of the stable of equilibrium point and the permanence of system. We extend the model to spatial field in order to studying the space dynamic of the model. This dissertation is organized as follows:1. Our main purpose in this paper is to study a model,which introduced the environmental carrying capacity K to a class of predator-prey system with stage of prey,then we obtain a autonomous model and a nonautonomous model. We assume that prey population censored Logistic equation. We discuss the boundedness and stability of the autonomy model,and obtain the sufficient condition of local stability of equilibrium point E*of the transformed model. Then we took a set of values of the model parameters were simulated. We discuss the permanence of system in the nonautonomous model,and obtain the sufficient condition of the permanence of the nonautonomous model.2. Then our main purpose is to study the stability of system that caused by population diffusion between two patches,and we simulate by using density dependence on the migration rules. We assumed there were two population on each two patches,the population censored the autonomous model in each patch. Considering the three situation diffusation between the two patches:(1)Only adult prey individual diffuse,(2)Only the predator individual can diffuse,(3)Both of them diffuse. We obtain that the dispersal of the adult prey impact on system is small; while the dispersal of the predator will cause the different effects in two patches of system:Chaos or stability. The study shows chaos are caused by the periodic oscillation of population in simulation.3. The intraspecific competition is introduced into prey species in the predator-prey model. We simulate by using Cellular Automata in Two-dimensional spatial grid,and obtain that the risk of species extinction reduce,when the competition gets bigger,that reason is the effect of migration between patches; when the competition gets smaller,the results of the system is similar to the system witch without spatial migration. And we establish a visual interface to study different parameter in simulation.