Research On Dynamical Properties Of Several Stochastic Biological Systems With Time Delay And Lévy Noise

With the rapid development of economy,the exploration and management of biological resources have been and will always be the focus of people's attention.The dynamical properties of ecosystem have been paid more and more attention by scholars.In practice,the biological system is always affected by various stochastic perturbations,and there is always time delay in the development of the system.These are the factors that must be considered in the modeling.In this paper,based on the real world,several biological systems with stochastic noise and time delay are instructed in this paper.By using stochastic comparison theorem,It(?) formula,the Lyapunov functional method and some mathematical inequalities,the permanent in time average,stability in distribution of above systems and the optimal harvesting effort are studied.All the main results are verified by numerical simulation.The main content of the article is as follows.In the first chapter,the research background,research significance,research status at home and abroad and the main content of this article are introduced.In the second chapter,some preliminary knowledge,such as the relevant lemmas and definitions of stochastic biological system are presented.In the third chapter,in view of the effects of stochastic noise and constant time delay,a stochastic three-population predator-prey system with constant time delay and Lévy noise is established.The almost sure existences,uniqueness of the global positive solutions of the system are discussed by existence theory of solutions of stochastic differential equations.By applying It(?) formula and Lyapunov functional method,the sufficient conditions of the permanent in time average and extinction of all species are established.The stability in distribution of the system is also analyzed.Under some certain assumptions,the sufficient conditions for the optimal harvesting effort are established.Finally,numerical simulation is given with MATLAB to verify the main conclusions.In chapter four,on the basis of the model in the third chapter,in view of the influence of varying time delay and stochastic perturbation,a stochastic predator-prey system with distributed time delay is established.By using the comparison theorem of stochastic differential equations and the technique of stochastic analysis,the permanent in time average and extinction of all species are discussed,and the sufficient conditions for the stability in distribution of the system are established.In addition,the results are verified by numerical simulation,and the effects of Lévy noise and distributed time delay on the system are further discussed,and some suggestions for the system control are given.In chapter five,a stochastic competitive model with distributed time delay and Lévy noise in polluted environment is established.Combined with the actual conditions,the permanent in time average and extinction of the population are studied.By comparing the polluted system with the non-polluted system,the important effects of the polluted environment and the Lévy noise on the system properties are discussed.Finally,the results are further verified by numerical analysis.Our main results obtained in this article enrich the dynamical properties of stochastic biological system,reveal the effects of time delay and Lévy noise when the intensity reaches a certain level,and provide a theoretical basis for the development and sustainable utilization of biological resources.