Robust Stability For Lotka-Volterra Systems With Infinite Distributed Delays

This paper is concerned with the robust stability and partial robust stability of a class of Lotka-Volterra systems with infinite distributed delay and the stochastic robust stability of a class of stochastic Lotka-Volterra systems with infinite distributed delay.Firstly,the research background of Lotka-Volterra systems and the randomization of Lotka-Volterra systems were introduced.Secondly,the concepts of stability,asymptotic stability and global asymptotic stability of delay differential equations were given firstly.Then some theory on probability and delay stochastic differential differential equations were introduced.Thirdly,a class of Lotka-Volterra systems with infinite distributed delay were studied.Some sufficient conditions were obtained for the globally asymptotic robust stability and partial robust stability of the system by constructing Lyapunov functionals,using Lyapunov-LaSalle theorem and interval dynamic system stability theory.Finally,a class of stochastic LotkaVolterra systems with infinite distributed delay were studied.Some sufficient conditions were obtained for stochastic robust stability of the system by constructing Lyapunov functional and using the It(?) formula.