Dynamic Analysis Of Several Kinds Of Predator-Prey Models With Impulsive Effects

It is well-known that the impulsive differential equations have been deeply investi-gated.Their theory is not only considerably richer than that of ordinary differential equa-tions without impulses, but also more adequately represents many mathematical simulation of such processes and phenomena. It has been widely existed in mechanical vibration, ce-lestial mechanics, celestial mechanics, economics, aerospace technology, feedback control, ecology, engineering technology etc. So, studying the properties of the solutions of impulsive differential equations has important practical significance.In order to further understand the application of differential system, this dissertation separately discuss several types of differential equations with delays and impulsive effects, and delay effects, some theories and approaches related to discrete dynamics, impulsive dynamics and different research methods are used to investigate dynamical behaviors including the existence and globally asymptotic stability of periodic solutions, extinction, and all kinds of complexities, and meanwhile the possible effects of delay and impulse on the dynamical behaviors are discussed. The whole thesis is devided into four chapters..In chapter1, we simply offer the development and background for periodic solutions, delay differential equations, impulsive differential equations, meanwhile list the research method of almost periodic solutions. We will give the question which will be discussed and necessary prior knowledge in this dissertation.In chapter2, we consider a delayed stage-structured predator-prey model. By use of the discrete dynamical system determined by the stroboscopic map, we obtain a predator-extinction periodic solution and sufficient conditions of the global attractivity. By using the theory on delay functional and impulsive differential equation, we obtain sufficient condition for the permanence of the system.In chapter3, we investigate impulsive harvesting threshold on a predator-prey model. We prove that all solutions of the investigated system are uniformly ultimately bounded. The conditions of the investigated system are obtained. Our results provide reliable tactic basis for the practical biological resource management,at same time, enrich the theory of impulsive differential equation. In chapter4, as this paper’s end of part, we have summarized the paper and proposed several questions which were worth further Considering.