The Semi-continuous Dynamical System And Its Applications In Population Dynamics

In this dissertation, we study the semi-continuous dynamical system and its applications inpopulation dynamics. We discuss some population dynamical models with state dependentimpulsive, and give sufficient conditions for the existence and stability of the order-oneperiodic solution of the models. Furthermore, we illustrate our main results by numericalsimulations. The dissertation has six chapters.The first chapter introduces the background and main research works of thesemi-continuous dynamical system in population dynamics, and summarizes our main results.The second chapter gives the related theory about semi-continuous dynamical system andsome preliminary knowledge.In the third chapter, we propose a two species competitive Lotka-Volterra system with statedependent impulsive effects. By the successor function method and analogue of Poincarécriterion, we obtain sufficient conditions for the existence and the orbital asymptoticalstability of the order-one periodic solutions in the system. Moreover, we give numericalsimulations to illustrate our main results.In the fourth chapter, we propose a kind of predator and prey system with state dependentimpulsive effects which the predator has orther food source. We give sufficient conditions forthe existence and the orbital asymptotical stability of the order-one periodic solutions in thesystem, and verify our main results by numerical simulations.In the fifth chapter, we propose a kind of predator and prey system with state dependentimpulsive effects which the prey can migrate from the outside world. We get sufficientconditions for the existence and the orbital asymptotical stability of the order-one periodicsolutions in the system, and verify our main results by numerical simulation.In the sixth chapter, we give a summary and the outlook of the dissertations.