Abstract
In this paper, a stochastic cooperative predator-prey system with Beddington-DeAngelis functional response is proposed. By constructing Lyapunov functions, we demonstrate the existence of global positive solution, which is stochastically bounded and permanent. In addition, under some specific conditions, the solution of this stochastic system is globally asymptotically stable, which means that the properties of the solution will not be changed when the stochastic perturbation is small. Finally, the influence of the stochastic perturbation is demonstrated by simulation.
Highlights
As an important branch of ecology science, population ecology has become a systematic discipline where mathematics is thoroughly applied
We introduce stochastic perturbation into the intrinsic growth rate
We will study the stochastic predator-prey system of one predator feeding on two prey species with Beddington-DeAngelis functional response
Summary
As an important branch of ecology science, population ecology has become a systematic discipline where mathematics is thoroughly applied. Various species of prey coexist in nature, so the multiple species predator-prey system simulates the actual situation better This has been neglected in many existing studies [ , ]. We investigate the following cooperative predator-prey system of one predator feeding on two prey species with Beddington-. We will study the stochastic predator-prey system of one predator feeding on two prey species with Beddington-DeAngelis functional response. Lemma For any initial value x > , y > , z > , system ( ) has a unique positive local solution (x(t), y(t), z(t)) for t ∈ [ , τe) almost surely (a.s.), where τe is the explosion time. We will discuss how the solution varies in R + more detail
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