Analysis Of Predator-prey Models With General Holling Functional Response And Impulsive Effects

It is well-known that many real world phenomena and human activities dohave impulsive effects. In this thesis, based on impulsive differential equations,we establish and investigate a general Holling functional response pest-naturalenemy model periodic releasing natural enemies and spraying pesticide at differ-ent fixed time, A three species food chain model with general Holling functionalresponse and periodic constant impulsive perturbations on the top predator, andThe dynamics of a predator-prey model with general Holling functional responseand the predator population with mutual interference concerning impulsive con-trol strategy. Mathematically, we use a combined approach of discrete dynamics,continuous dynamics and impulsive dynamics to investigate various dynamicalbehavior of the systems we consider. From the viewpoint of the biology, themathematical results are full of biological meanings and can be used to providereliable foundations for making decisions.In chapter 1, we present our motivations, gist and signification for our paperand summarize the prior work on predator-prey, model with Holling type func-tional response and impulsive effects. Next, in chapter 2, some useful lemmas,definitions and fundamental theorems are given in the preliminaries.In Chapter 3, according to the fact of periodic biological and chemical controlfor pest control and the effect of pesticide on natural enemy, we construct ageneral Holling functional response predator-prey system concerning impulsivecontrol strategy-periodic releasing natural enemies and spraying pesticide atdifferent fixed time. By using Floquet theory, Comparison theorem of impulsivedifferential equation and analytic method, we investigate the dynamics of thesystem in detail. We obtain the conditions of asymptotical stability of the pest-eradication periodic solution and permanence of the system.In chapter 4, with the application of the possible exterior effects under which the population densities change very rapidly. (An impulsive increase of the toppredator population density is possibly by artificial breeding of the species orreleasing some species) We establish A three species food chain model with gen-eral Holling functional response and periodic constant impulsive perturbationson the top predator, investigate the dynamics of the system under the effects ofimpulsive perturbations generally, and establish condition for extinction of pestand the permanence of the system. We also proved boundary of the system.In chapter 5, based on a predator-prey model with general Holling func-tional response and the predator population with mutual interference, we takeinto account the possible exterior effects by releasing predator(natural enemy)atfixed time. The dynamics of the system become more complicated because of theeffects of exterior forces and mutual interference. And we found that the litera-ture on this system has never been seen. In this paper, By using Floquet theory,Comparison theorem of impulsive differential equation and analytic method, weinvestigate the dynamics of the system in detail. We obtain the conditions forasymptotical stability of the pest-eradication periodic solution and permanenceof the system.