Study On Asymptotic Properties Of Some Stochastic Population Models With Environmental Noises

There are uncertainty and stochastic noises among our human-being's living environ-ment,so it is of some theoretical research meaning and applying value on creature protection and ecological balance keeping by studying on the dynamical behaviors of the stochastic population systems with environmental noises.In this dissertation,we focus on several stochastic population systems with environmental noises and consider about several asymp-totic behaviors,such as consensus,persistence and extinction,stochastic ultimate bounded-ness,the properties of period solution,the exponential stability of numercial solutions etc.Our specific contents are as follows:(1)Under different topological structures and proper control protocols,the sufficient conditions to obtain the finite-time consensus of Lotka-Volterra model with stochastic envi-ronmental noises input control are discussed.Based on the basic principle of Graph Theory,the interactions among species can be classified into directed graph and undirected graph,then combining theories of stochastic differential equation and constructing feedback con-trol functions,the sufficient conditions to attain finite-time consensus for populations under different topologies are obtained.Finally,the convergence time in probability sense are giv-en.(2)The asymptotic behavior of resource competition models under environmental noises are studied.Considering that growth rate and mortality rate are both influenced by differ-ent white noises,the stochastic resource competition model are proposed.Firstly,the exis-tence of the system's positive solution are obtained.Then by using of Lyapunov functional method,stochastic comparison theory,strong law of large numbers of Martingale and sev-eral essential inequalities,the asymptotic behaviors are discussed,such as persistence and extinction,stochastic ultimate boundedness and path-wise estimation.Finally,the effective-ness of conclusion and the rationality of conditions are illustrated by several examples and some numerical experiments.(3)Three-species non-autonomous stochastic Lotka-Volterra food web system in pollut-ed environment is proposed,and the existence of the system's positive periodic solutions is established,which is proved by constructing proper Lyapunov function.Then the extinction property and its threshold between persistence and extinction is discussed by using of Ito formula and strong law of large numbers of Martingale,and the sufficient condition of expo-nential stability of equilibrium point almost everywhere is obtained.Finally,the conclusions are tested by several numerical simulations.(4)Asymptotic properties of a kind of age-structured population system are studied.The effect of spacial diffusion and stochastic noises are considered in the system,then the existence and uniqueness of solution are obtained by constructing Lyapunov function and by use of the basic theory of stochastic analysis.Furthermore,the numerical calculation of the Euler form is given,which is under the condition weaker than Lipschitz and linear growth,and then,the exponential stability of numerical solution is studied.Finally,conclusions are illustrated by several simulation examples.