Dynamics Analysis Of Predator-prey System With Beddington-Deangelis Functional Response

The survival and development of biotic population were influenced by its livingenvironment, we concerned on topic of how to keep long-term thriving of differentorganisms under the limit ecological resources condition. Second, since the ecologicalenvironment was excessive intervention and polluted by human activities, those factorsthreatened the diversity of population, some species even tend to be extinct. Because thesuperiority of Beddington-DeAngelis functional response in describing the relationshipbetween the predator and prey, the predator-prey system established under Beddington-DeAngelis function response were widely attention by scholars; On the other hand, inorder to deeper reveals interactions between predator and prey species, we should considerthose factors which influence the persistent existence of species, these factors reflected inpredator-prey system models were harvesting or investing, diffusion, time delay, stagestructure and so on, so as to make models more in line with the actual ecological systems.On the basis of previous studies, taking together a variety of factors, this paper consideredthree kinds of predator-prey system with Beddington-DeAngelis function response, westudied the dynamics behaviors of the system, studying of the system had importanttheoretical and practical significance. Part of conclusions improved or popularized theprevious conclusions of the published literature, and provided theory basing for furtherprotection, development and use of biological resources.This paper first expounded the advantage of Beddington-DeAngelis function inreflecting the relations between predator and prey, as well as the realistic meaning ofharvest, release, time delay, stage structure in biological system. The research background,significance and research status of predator-prey system with these factors were explained,and put forward the main work to be done in this paper.Apredator-prey system with Beddington-DeAngelis functional response and selectiveharvesting rates of predator specie was given in the second chapter, where prey andpredator both had linear density dependent. We used ordinary differential equationscharacterization and stability to study the existence and uniqueness of positiveequilibriums, deriving the sufficient conditions of its global asymptotic stability and localasymptotic stability, an optimal taxation policy was obtained by Pontryagin Maximumprinciple.A non-autonomous predator-prey system with nonlinear diffusion and Beddington-DeAngelis functional response was studied in the third chapter, which had continuous and discrete time-delay at the same time. We proved this system was persistent existence underappropriate conditions, and sufficient conditions of the globally asymptotic stability ofpositive periodic solution were obtained, a numerical example shows the results.In the fourth chapters, we gave a three population predator-prey system with stagestructures, using the comparison theorem and analysis method, the sufficient conditionswere gained for the persistent existence of the system.We applied the numerical simulation to verify the conclusions of the theorems, andgot numerical simulation diagrams which reflecting systemic state.