The Stability Analysis Of Stochastic Ecological Systems With Impulsive

With the development of society and the rapid growth of the world economy,ecological and environmental issues have been increasingly focused on by humans.In recent years,deterministic biological population systems have attracted widespread attention.However,many models of biological population in real life may be disturbed by random factors.Therefore,it is important to study the stochastic biological population model to determine whether environment noise and pulses have an impact on the population system.In this paper,several types of stochastic biological population models based on the effects of pulses and stochastic factors are established.Stochastic differential equation comparison theorem,Lyapunov functional,It? formula,and some analytical techniques are applied to study some dynamic properties on our established systems,such as the existence and uniqueness of global positives solutions,stochastic persistence,and existence of random periodic solutions.Finally,the results were verified by numerical simulation.The paper is composed of the following five chapters.Chapter one mainly introduces the research background,research significance,research status at home and abroad and the main works of this paper.Chapter two is the preparatory knowledge,which mainly gives the main definition and some related lemmas.Considering that the population is affected by impulse and random factors,a class of impulsive predator-prey system with non-linear capture is established in chapter three.The theory of impulsive differential equations,Lyapunov function,and It? formula are used to discuss the existence and uniqueness of the global positive solution of the stochastic system,the existence of the random periodic solution,and the almost global attractivity of the random system.The determination criteria for the existence of the periodic solution of the system is established later.Finally,numerical analysis of the random periodicity and almost global attractiveness of the system solution through numerical simulation is given to reveal the effects of impulse and random disturbance on biological population.Chapter four proposes a class of impulse predator-prey model with Holling-II type functional response.By adding the mutual interference constant m to this model and applying related theories to explore sufficient conditions for the existence of random periodic solutions and the average duration of time when m(28)1 and 0(27)m(27)1,and the results show that white noise and pulse interference have important effects on population dynamics.Finally,the validity of conclusions obtained is further verified by examples and numerical simulations.In chapter five,a class of Holling-III ratio-dependent stochastic predator-prey system with impulsive perturbations is established.By means of the stochastic differential equation comparison theorem and the It? formula,we obtain that there is a globally unique positive solution to the stochastic system,and present the conditions for the random persistence of the system and for the tendency of the population to extinction,and discuss the final randomness of the system.Finally,conducting simulated analysis to the theoretical results shows that white noise and pulses can affect the population.The results own preferable theoretical significance.Above all,by using the It? formula and constructing some appropriate Lyapunov functional,this paper obtains properties such as the existence,random persistence,andextinction of random periodic solutions of several types of ecosystems.The obtained results generalize some existing theoretical results,and enrich the stochastic ecosystem and the theory of impulsive dynamic systems.