Research On The Asymptotic Properties Of Population System With Two Kinds Of Environmental Noises

The sustainable survival of biological population is closely related to the balance and stability of ecological system.Biodiversity has been concerned by the whole society since the concept was proposed,which plays an indispensable role in the sustainable development of human beings.In the real life,biological population is often affected by environmental noises.Therefore,It is important to fully understand how environmental noises affect the population.Most of the existing research is about population models with a kind of noise,which lacks analysis of stability.This paper mainly studies the stochastic population model with net birth noise and interaction noise,and takes stability of the system into consideration.By choosing appropriate Lyapunov functions and using It(?)'s formula,exponential martingale inequality,strong law of large numbers and boundedness of polynomial functions,this paper studies the effects of the net birth noise and the interaction noise on the asymptotic properties of population system,analyzes the long-term dynamics.The specific work of this paper is as follows.Firstly,we give a sufficient condition for the existence of a global positive solution about the stochastic population system,prove that the solution of the system has stochastic persistence,stochastic boundedness and polynomial growth rate,reveal that the large enough net birth noise can lead to population extinction.The results show that the asymptotic properties except extinction mentioned above are only related to the interaction noise,but not to other parameters.Then,we analyze the asymptotic properties of the system with the relatively small net birth noise,give a sufficient condition for the existence of stationary distribution.By the ergodicity theorem,we prove that the second moment of the stationary distribution is finite,and give the expression of the relationship between expectation and variance.Lastly,we generalize the stochastic population model to an abstract stochastic differential equation,and study its global attraction,stochastic boundedness,asymptotic path estimation and stability.