The Study For The Dynamics Behavior Of Several Population Dynamical Systems

The need for describing natural system impels the evolution of mathematical biological models. In recent years, the research in mathematical biology which modeled by normal differential equations are mainly concentrated on two branches:continuous dynamical systems and impulsive dynamical systems. Especially, impulsive systems are suitable for the mathematical model of evolutionary processes which experience a change of state abruptly due to instantaneous perturbations.In this thesis, we considered models of several population dynamical systems and discussed their dynamical behaviors, including the exist of positive periodic solutions, the permanence and extinct of the system etc, This thesis contains for parts:The first part is introduction, The background and significance of the research on this topic is stated briefly, and some preliminaries have been given.In the second chapter, the model of predator-prey system with impulsive effect and integrated pest control has been formulated and investigated. Sufficient condition for permanence and extinct are obtained.In the third part, a predator—prey model with time delay and stage-structure in prey is considered, the existence of multiple positive periodic is established by using the continuation theorem of coincidence degree theory.The fourth part considers a model with delayed growth response and nutrition recycling in the polluted environment, Sufficient condition for permanence and extinct are established via impulsive differential theory and compute technique.