The Qualitative Analysis Of Predator-prey Model With Feedback Control And Diffusion

The research on the population dynamic models with feedback control contribute to promote the harmonious development between man and nature and maintain the dynamic balance of ecosystem.But the research on the predator-prey models about partial differential equations with feedback control and diffusion are limited related to the traditional population dynamic models.So the results of the existence of periodic solutions and stability for the predator-prey models about partial differential equations with feedback control and diffusion were proved by using the comparison theorem of differential equation,the method of upper and lower solutions,the Schauder fixed point theorem as well as Lyapunov stability theory on the basis of the seniors' research of the predator-prey models about the ordinary differential equations.The four parts in this thesis as follows:In the first part,a predator-prey model about partial differential equations with feedback control and diffusion is studied.We should translate the partial differential equations into the ordinary differential equations first,then we use the comparison theorem of differential equations to get the sufficient conditions of the uniform boundedness for the model,and the existence of periodic solutions are proving by using the Schauder fixed point theorem but ensure the uniform boundedness for the model.At last we should use the Lyapunov stability theory to get the sufficient conditions of the global asymptotic stability for the system.In the second part,a ratio-dependent predator-prey model about partial differential equations with feedback control and diffusion is studied.In this chapter,the ratio-dependent factor will be added into the model on the basis of the study of the first part to make it more coincident with the actual situation.We should use the comparison theorem of differential eq uations,the skills of inequalities enlarge and shrink to get the sufficient conditions of the uniform boundedness for the model first,then there are at least one strictly positive periodic solution T-were proving by using the Schauder fixed point theorem but ensure the uniform boundedness for the model.At last we can get the sufficient conditions of the global asymptotic stability for the system by constructing proper Lyapunov functions and using Barbalat lemma.In the third part,we further study a class of delay predator-prey model about partial differential equations with feedback control and diffusion.In this chapter,the time delay will be added into the model on the basis of the study of the second part because of the impacts of space factors and time factors on population dynamic models,and we use the improved ways to get the sufficient conditions of the existence of periodic solutions and stability for the model.In the fourth part,we further study three-species interacting food-chain model on the basis of the study of two-predator and one-prey model in the former three chapters.We should use the comparison theorem of differential equations to get the upper and lower bounds of each population density in order to deduce the sufficient conditions of the uniform boundedness for the model and use the method of upper and lower solutions and Lyapunov stability theory to study the stability of the model.At last,the simulation results of software MATLAB prove the validity of the fundamental research.