Dynamics of a Stochastic Delayed Predator-Prey System with Beddington-DeAngelis Functional Response

Abstract

This paper is concerned with a stochastic predator-prey system with Beddington-DeAngelis functional response and time delay. Firstly, we show that this system has a unique positive solution as this is essential in any population dynamics model. Secondly, the validity of the stochastic system is guaranteed by stochastic ultimate boundedness of the analyzed solution. Finally, by constructing suitable Lyapunov functions, the asymptotic moment estimation of the solution was given. These properties of the solution can provide theoretical support for biological resource management.