Stationary probability density and noise-induced transitions in a stochastic host-generalist parasitoid model

Abstract

In this paper, we study the dynamical behavior of a stochastic host-generalist parasitoid model with Holling II functional response. First, by constructing a suitable Lyapunov function, we prove that the stochastic system has a unique ergodic stationary distribution under certain condition. Second, we analyze the stationary probability density when the corresponding deterministic system has a unique stable positive equilibrium. The original stochastic system is transformed to an It[Formula: see text] average diffusion system by using Taylor expansions at the positive equilibrium point, polar coordinate transformation and stochastic average method. Then the stationary probability density is obtained by solving the Fokker–Planck equation of the average diffusion system. Finally, we explore noise-induced state transitions between two random attractors in the bistable regions: (i) between two internal stable equilibria; (ii) between an internal equilibrium and a limit cycle. The critical noise intensity for which the state switching occurs is estimated by calculating confidence ellipses. The results show that large environmental fluctuations can obviously affect the stability of ecosystems, and cause transitions between high and low biomass of the hosts and the generalist parasitoids.