Asymptotic behavior and numerical simulations of a Lotka-Volterra mutualism system with white noises

Abstract

Abstract In the present paper, a stochastic mutualism model subject to white noises is established. We first investigate the existence and uniqueness of globally positive solution of the stochastic model. Then we study its asymptotic behavior, such as stochastic permanence and extinction, and estimate the limit of the average in time of the sample paths of every component. We also show that the stochastic system is globally attractive under some appropriate conditions. Finally, numerical simulations are presented to justify the analytical results.

Keywords

• mutualism system
• white noise
• stochastic permanence
• extinction
• global attractivity