The Asymptotic Behavior Of The Stochastic Gilpin-Ayala System With Delays

In this paper, the asymptotic behavior of stochastic Gilpin-Ayala system withdelays was discussed. In chapter three, the stability of the stochastic Gilpin-Ayala systemwith delays was investigated. The conditions to guarantee the stability of an equilibriumstate were given by using the Lyapunov functional method, Ito integral rule and structuringa right Lyapunov function. In chapter four, some asymptotic behavior of the solutions ofthe stochastic Gilpin-Ayala system with delays was studied. Under some conditions, theexistence and asymptotic estimation and pathwise estimation for the global positive solutionsof the stochastic Gilpin-Ayala system with delays were discussed by using Lyapunov functionalmethod and the nature of the polynomial function. Some special related conclusions wereobtained for the stochastic Gilpin-Ayala system with delays.