Global asymptotic stability of a stochastic Lotka–Volterra model with infinite delays

In this paper, sufficient criteria for global asymptotic stability of a general stochastic Lotka–Volterra system with infinite delays are established. Some simulation figures are introduced to support the analytical findings.

► A stochastic stochastic Lotka–Volterra system with infinite delays is proposed.
► The stochastic model will also be globally stable if the noise is not large.
► Simulation figures support the analytical findings.
► Some classical deterministic results are extended to the stochastic cases.