Asymptotic behavior of a food-limited Lotka-Volterra mutualism model with Markovian switching and Lévy jumps

In this paper, we investigate a food-limited Lotka-Volterra mutualism model with Markovian switching and Lévy jumps. We present the analysis and the criteria of the asymptotic behavior for this perturbed model via Lyapunov functions. Our results show that both colored noise and Lévy noise have important effects on the survival and extinction of the species.