Stability of a stochastic discrete mutualism system

Abstract

Abstract Under the assumption that stochastic white noise perturbations are directly proportional to the deviation of the state from the equilibrium states of a continuous mutualistic model, we use the Euler–Maruyama discretization method to obtain a two-species stochastic discrete mutualism model. For this stochastic model, we establish conditions on the asymptotic mean square stability of the positive equilibrium state and the almost sure asymptotic stability of the three boundary equilibrium states. The theoretical results are supported with numerical simulations.

Keywords

• Asymptotic mean square stability
• Stochastic discrete mutualism model
• Linearized method
• Lyapunov functional method