Analysis Of Dynamic Behaviors On Two Predator-prey Models With Stage Structure And Birth Pulse

The relationship between predator and prey is one of basic relationships amongspecies, which is one of the most prevalent interactions in the nature. Recently, due tothe ecological problems has drawn great attention and combined with the complexityof ecological relationship provides researchers with rich research object, thepredator-prey models have attacted more attention.In this paper, according to the population dynamics and the relevant theoreticalknowledge of the impulsive dynamical equations, we establish two classes ofpredator-prey systems with stage structure and birth pulse. Based on some relatedtheorems and lemmas, the dynamic behaviors including stability of extincte periodicsolutions and permanence of systems are discussed, respectively. There are threechapters in this thesis.In Chapter1, the backgrounds and present development of the system investing-ated about population and pulse dynamics as well as the main work done in this thesisare given.In Chapter2, consider the impulsive effect on the stage-structured predator-preymodel with bith pulse in the predator. The predator-prey with pulses at the same timeand different moment are investigated, respectively. By using the comparisondifferential theorem, we obtain both the sufficient conditions of global asymptoticstability of the mature prey-extinction periodic solution and the permanence of thesystem. At last, we give numerical simulations for our main results and analysis theoptimal time of pesticide applications.In chapter3, we establish a two prey-predator system with stage-structure andbirth pulse for predator. According to the Floquet theorem, small amplitude perturbati-on methods and the relative theorems of impulsive differential equation, the sufficientconditions of global asymptotic stability of the prey-extinction periodic solutioin andthe permanence of the system are obtained.