Research On Dynamical Properties Of Stochastic Biological Systems With Time Delay

Random noise,not only ubiquitous,but also can describe the random disturbance in production better.Introducing the stochastic differential equation theory into the study of population ecosystem has become an important topic of system dynamics.Therefore,basis on considering random noise,time delay,environmental pollution and other factors,this thesis studies three kinds of population ecological models by constructing Lyapunov function,adopting It(?) formula and some random analysis methods.The main contents are as follows.Chapter one mainly introduces the research background,research significance,research status at home and abroad and the main works of this thesis.The second chapter is preparatory knowledge,which mainly gives the relevant lemmas and definitions of this article.In chapter three,considering the effect of random disturbances,a kind of stochastic predator-prey system with time delay effect and Beddington-DeAngelis type functional response is studied through modeling.The almost sure existence,uniqueness and stochastic boundedness of the global positive solutions of the system are proved by adopting the existence theory of the solutions of stochastic differential equations.The asymptotic moment estimation is given by constructing an appropriate Lyapunov function.In chapter four,in view of the extensive influence of polluted environment on the population,the dynamic behaviors of a kind of stochastic one-predator-two-prey population model with time delay effects in the polluted environment is modeled and studied,which involve the almost existence of the global positive solution of the system under some certain conditions,the sufficient conditions for the time averaged persistence,and the almost everywhere global attractiveness of the system by making use of stroboscopic mapping and stochastic analysis.The main results of this chapter are verified by numerical simulation and the dynamic properties of the system are further discussed.In chapter five,considering the influence of colored noise on the biological population,the optimal capture problem of the reciprocal model with Lévy noise and time delay effect in polluted environment is studied.Firstly,the time average persistence of each population under certain conditions is studied.Based on these studies,then using the ergodic method,the sufficient and necessary conditions for the asymptotically stable in distribution,and the sufficient and necessary conditions for the existence of the optimal acquisition strategy are established.Finally,the theoretical results are verified by numerical simulation,and further discuss on the influence of Lévy noise on the dynamic properties of the system are given.The results of this thesis enrich the theory of stochastic ecosystem,reveal the influence of stochastic disturbance and time delay on the stability of the system,and provide a certain theoretical basis for the development and utilization of biological resources.