The Positive Periodic Solutions And Almost Periodic Solutions For Several Predator-Prey Models In Ecology

Population ecology is the most basic branch of ecological mathematics, and is alsoearly development, most mature branches. In recent years, the predator-prey relationhas become a very important part in population ecology Because the predator-preyrelation has a great value in application, it has received more and more attention ofmany scholars.In this paper, by the results of Mawhin coincidence degree theory, fraction trans-formation skills, the basic theory of impulsive differential equations and the method ofconstructing Lyapunov function in stability theory of ordinary differential equation, weresearch the dynamic features of several predator-prey model in ecology. The paperconsists of three chapters.Chapter1introduces the backgrounds and significance of our studies, main workof this paper, preparing knowledge.Chapter2considers the existence and global attractivity of positive periodic solu-tion to a predator-prey model with mutual interference and Holling III type functionalresponse. By utilizing the Mawhin coincidence degree theorem and constructing a suit-able Lyapunov function, we present some sufficient conditions which guarantee theexistence and uniqueness of global attractive positive periodic solution. Lastly, by nu-merical simulation for the model we verify main results. The conclusions improve themain results of the references.Chapter3mainly discusses a predator-prey system with Beddington-DeAngelisfunctional response and impulsive effect. In addition, we consider the effection ofvariable delay for the model. By using the Mawhin coincidence degree theorem, weestablish some criteria to guarantee the existence of positive periodic solutions. Evenunder the non-pulse circumstances, our results generalize and improve some knownresults.Chapter4considers the existence of a unique globally attractive almost periodic solution to a predator-prey model. On the basis of Chapter2, we consider the effectionof variable delay for the model. By utilizing the comparison theorem of the differentialequation and constructing a suitable Lyapunov functional we present some sufficientconditions which guarantee the existence and uniqueness of global attractive almostperiodic solution. By numerical simulation for the model we verify main results.