Analysis of a mutualism model with stochastic perturbations

TL;DR

This paper investigates a stochastic mutualism ecological model, establishing conditions for its long-term behavior, including extinction, persistence, and boundedness, supported by theoretical analysis and illustrative figures.

Contribution

It provides new mathematical conditions for extinction and persistence in a stochastic mutualism model, extending previous deterministic analyses.

Findings

The solution is stochastically bounded and uniformly continuous.

Conditions for system extinction are established.

Conditions for system persistence are identified.

Abstract

This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied. Moreover, we show that the solution is stochastically bounded, uniformly continuous and stochastic permanence. The sufficient conditions for the system to be extinct are given and the condition for the system to be persistent are also established. At last, some figures are presented to illustrate our main results.