Stochastic Lotka–Volterra mutualism model with jumps

Abstract

The existence and uniqueness of the global positive solution are proved for the system of stochastic differential equations describing a two-species Lotka–Volterra mutualism model disturbed by white noise, centered and noncentered Poisson noises. For the considered system, sufficient conditions of stochastic ultimate boundedness, stochastic permanence, nonpersistence and strong persistence in the mean are obtained.

Keywords

• Stochastic Lotka–Volterra mutualism model
• global solution
• stochastic ultimate boundedness
• stochastic permanence
• nonpersistence
• strong persistence in the mean