| Along with the technical development of modern science, the research of many science realms, for example automatic control,ecosystem system, genetics, economics, physics, communication theories etc.,involve to functional differential equation(that is differential equation with time delay).But the period solution,uniform permanence,global attractivity always is a few important branch of the research of functional differential equation theory.Particularly ,in the last 30 years,it obtain overall developments and abundant results.This thesis directs towards some open problems and conjectures by Xu and Li.We consider some properties of posive solutions and posive equilibrium position of several kinds of predator-prey models with Holling type functional response ,for example, boundedness and persistence,global asymptotic stability,uniform permanence etc.Some known results are improved,and some conjectures by Xu and Li are proved partially here.We also investigate the more general situation of the problems by Xu and Li,and push forward the study of the problems.The whole thesis is composed of four chapters.In Chapter 1, the background and some related researching situations of the biological dynamic system are briefly reviewed, some problems are raised which will be investigated and some concepts and notations are listed which will be used in our paper.In Chapter 2, by using the continuation theorem of coincidence theory, we discuss the existence of positive periodic solutions for a class of nonautonomous ratio-dependent three species predator-prey system.In Chapter 3, a predator-prey model with Hollingâ…¢functional response and stage structure for prey is investigated, we derive sufficient conditions for the uniform persistence and impermanence of the model.At last, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of positive equilibria of the above model.
|
PDF Full Text Request