The Dynamical Analysis Of Several Kinds Of Impulsive Ecological Systems With Diffusion And Delays

With the development of society,ecological environmental issues are increasingly valued by humans.Recently,scholars have obtained the developmental changes of biological populations by studying the biological population model.The research results provide a key strategy for protecting endangered species,managing ecological resources,and maintaining ecological balance,which has important practical significance.Based on practice,a series of ecological model with impulsive,time delay and diffusion are proposed and researched in this paper.By using the theory of impulsive differential equation,coincidence degree theory,Lyapunov functional and some analysis techniques,the existence of solution,persistence and global attraction of system are investigated,which are verified by numerical simulation.The main content is as follows.The introduction mainly introduces the research background,significance,status and the main work of this paper.The preliminary knowledge introduces the main definitions and relevant lemmas of this paper.Considering the effects of infinite delay,an impulsive predator-prey model with infinite delay and discrete diffusion is established in the third chapter.By means of coincidence degree theorem,impulsive differential equation theory and Lyapunov functional techniques,the existence of periodic solutions is discussed.The criteria for system persistence and global attraction are established.Finally,the results are verified by numerical simulation,and the practical application value of the results is discussed.Considering the hibernation,a predator-prey system with impulsive diffusion and hibernation is established in the fourth chapter.By means of theorem of impulsive differential equation and stroboscopic map,the global attractiveness of the predator-extinction periodic solution and the persistence of the system are studied.Then,the rationality and effectiveness of the results are proved by numerical analysis.Finally,the influence of impulsive diffusion is discussed in detail and some suggestions for biological species management are given.Based on reality,a competitive system with infinite delay and discrete dispersal is proposed in the fifth chapter.By use of the theory of differential equations,Lyapunov functional,the criterion of the permanence and globally attractive for species are investigated,which revealed the competition relation of for each population.In the sixth chapter,a cooperative system with infinite delay and discrete diffusion is given.By utilizing the theorem of impulsive differential equations and coincidence degree theorem,the existence of periodic solution was studied.Then using Lyapunov function,the criterion of permanence and global attractivity is derived.Finally,an example is given to show the complex dynamics of this system.