The ergodic property and positive recurrence of a multi-group Lotka–Volterra mutualistic system with regime switching

In this paper, we consider a stochastic multi-group Lotka–Volterra mutualistic system under regime switching. It is well known that the population is forced to expire when the perturbation is sufficiently large. The main aim here is to investigate its ergodic property and positive recurrence by stochastic Lyapunov functions under small perturbation, which can be used to explain some recurring phenomena in practice and thus provide a good description of permanence. The mean of the stationary distribution is estimated. Simulations are also carried out to confirm our analytical results.