Dynamic Properties And Simulation Analysis Of Several Kinds Of Impulsive Predator-Prey System

In recent years,differential equation theories have been developed rapidly in the fields of control system and medical research,especially in the population dynamical system.Many scholars have also devoted themselves to the research of the ecosystem and have obtained good conclusions.In this paper,based on practical problems,by constructing practical models,some dynamical properties of four kinds of predator-prey systems are studied.The main contents are as follows:In the first chapter,the research background,significance and research status of predator-prey system are introduced.In the second chapter,some notations,main definitions and lemmas are introduced.In the third chapter,considering the effects from birth pulse and time delay on evolution process of ecosystem,a class of time-delay predator-prey system with birth pulse and impulsive harvesting on the prey is established.By using comparison theorem,Lyapunov function,we study the related properties of the predator extinction periodic solution,and obtain the sufficient conditions of the persistence.Meanwhile,we use numerical simulations to verify the validity of the theoretical conclusions.Furthermore,if the mutual interference occurs between predators,some complicated dynamical behaviors are explored.In the fourth chapter,based on the stage structure factor of species,a class of predator-prey system with stage structure and impulsive effects is established.We prove the existence,stability,global attractivity and permanence of the system via the small amplitude perturbation,the Floquent theory,etc.Finally,the dynamical behaviors of the system are demonstrated by numerical simulation,which provides a reference for the protection of the ecosystem.In the fifth chapter,considering the interaction of environmental toxins,group defense and mutual interference,a class of predator-prey system with group defense and mutual interference in a polluted environment is established.By using differential equation theories,we investigate the properties of the prey extinction periodic solution and the persistence.Finally,time series diagrams and chaotic maps are obtained by model simulation.In the sixth chapter,considering the effects of multiple species coexistence and mutual interference,a class of multispecies predator-prey system with mutual interference and time delays is established.By means of the comparison theorem,Ascoli theorem and Lebesguedominated convergence theorem,we establish the sufficient conditions ofpermanence and investigate the existence of a unique almost periodic solution.By constructing a suitable Lyapunov function,we obtain that the positive almostperiodic solution is globally attractive.Finally,we give numerical simulations toindicate the complex dynamical behaviors of this system.In conclusion,by studying the properties of the above four kinds of predator-prey system,we get a series of theoretical results,which can provide strategies and suggestions for balance and development of the ecosystem,and has a good practical significance.