Dynamic Behavior Of Three Classes Of Stochastic Biological Population Models

Population dynamics is an important branch of the biological mathematics.Many scholars usually establish mathematical models to describe the evolution of species.Therefore,by using mathematical theories and mathematical methods,the dynamical behaviors of populations are investigated.Certainly,these results provide the theoret-ical values for the management of biological populations.Noting that population systems are often subject to environment with white noise.Therefore,in this paper,we mainly consider the effects of white noise on the population dynamic behaviors.Based on the deterministic Lotka-Volterra population models with Holling-type functional response,diffusion,time delay,and diffusion,we establish the corresponding stochastic population models.Furthermore,by constructing the appro-priate Lyapunov functions,applying the Ito formula and using the comparison theorem of differential equation,we discuss the dynamical behaviors of these stochastic models.Finally,we verify our results by numerical simulations.In chapter one,we introduce research background,research significance and the current research status about population dynamical models.Moreover,we give some basic definitions and preliminaries of the paper.In chapter two,by introducing stochastic perturbs to the deterministic Lotka-Volterra system with diffusion,we establish a stochastic competition population sys-tem.We prove there exists a global positive solution of the system by applying the Ito formula.Secondly,we discuss the stochastic ultimate boundedness of the system solution through constructing the appropriate Lyapunov function.Finally,we obtain a sufficient condition for the population extinction,and give a numerical example to verify our results.In chapter three,we consider a stochastic delayed predator-prey model with Holling-type ? type functional response.By constructing the suitable Lyapunov function and using the Ito formula,we discuss the existence of global positive solution of the sys-tem,and analyze the stochastic ultimate boundedness of the solution.At last,the asymptotic moment estimation of the solution is given.In chapter four,we discuss a random predator-prey model with diffusion and Holling-type ? functional response.We prove the global positivity of solution with the positive initial values.Moreover,we analyze the extinction and persistence in the mean of system by the comparison theorem of stochastic differential equation.The sufficient conditions,which guarantee the extinction and persistence in the mean of system,are obtained.Finally,numerical examples are applied to verify our results.In chapter five,we summary our works,and point out the shortcomings of the paper.Finally,we make a prospect for the future work.