Asymptotic stability of stochastic single-species model under regime switching

This paper investigates the stationary probability distribution of the well-known stochastic logistic equation under regime switching. Sufficient conditions for the asymptotic stability of both the zero solution and the positive equilibrium are derived. The stationary distribution of the logistic equation under Markovian switching is obtained by computing the weighted mean of the stationary distributions of its subsystems. The weights correspond to the limiting distribution of the underlying Markov chain.