Study On The Exact Controllability Of Stochastic Population Models

In this paper,we investigate the exact controllability of stochastic population mod-el by the theory of semigroups.The whole paper is divided into four parts.In Chapter 1,we briefly introduce the background and the significance of our research;Chapter 2 provides some fundamental definitions,marks and basic theories about stochastic pro-cesses and strongly continuous semigroups,which will be used in this paper.Chapter 3 is devoted to the exact controllability of nonlinear stochastic differential equations in abstract spaces.Here we suppose that the deterministic system is exactly control-lable.Our main results concern the exact controllability of the system by constructing appropriate control function.Chapter 4 of this paper is devoted to the exact control-lability of nonlinear stochastic population model with delayed birth process.By using the theory of nonlinear functional analysis,we establish sufficient conditions for the controllability of the relative model.