The Studies On Population Dynamical With Impulsive Perturbation

The need for describing more actual system impels the evolution of mathematical bi-ological models.In recent years,the researches in mathematical biology which modeled by normal differential equations are mainly concentrated on two branches:1)continuous bio-logical dynamical systems;2)impulsive semi-dynamical systems.The discussions of con-tinuous biological dynamical systems were main research direction in the past decades ,people find recently that continuous biological dynamical systems can not represent some natural phenomena and control behavior of human accurately;impulsive semi-dynamical systems then turn out to be the hotspot of mathematical biology because the relatively instantaneous behavior mentioned above can be described well in impulsive differential equations.Our three models in this paper which have different applicative background is of kind of differential system.In chapter 1,We introduce concisely some definitions and fundamental theories of differential equations and impulsive differential equations.In chapter 2,Based on biological control strategy in pest management, we construct and investigate a pest-epidemic model with impulsive control, i.e., periodic spraying mi-crobial pesticide and releasing infected pests at different fixed moments. By using Floquet theorem and comparison theorem, we prove that the pest-eradication periodic solution is globally asymptotically stable when the impulsive releasing infective pest more than the critical value P*.In chapter 3,In this paper,we investigated a three trophic level food chain system with periodic constant impulsive perturbations for top predator.Firstly,predator eradica-tions periodic solution of top predator are given.Afterward,by using comparison theorem of impulsive equation and Floquet theory,we prove that the predator eradications periodic solution is globally asymptotically stable when impulsive periodT is less than the critical value.In chapter 4,In this article,three species food chain system with impulsive perturba-tions and distributed time delay is investigated.Firstly,by using Floquet theory of impul-sive differential equation and comparison theorem,the global stability of predator eradi-cation periodic solution is considered.Secondly,we obtain the conditions which guarantee the permanence of three species.Finally,we analysis the effects of impulsive release for top predator on three food chain system.