Stability of a Beddington–DeAngelis type predator–prey model with trichotomous noises

Abstract

The stability analysis of a Beddington–DeAngelis (B–D) type predator–prey model driven by symmetric trichotomous noises is presented in this paper. Using the Shapiro–Loginov formula, the first-order and second-order solution moments of the system are obtained. The moment stability conditions of the B–D predator–prey model are given by using Routh–Hurwitz criterion. It is found that the stabilities of the first-order and second-order solution moments depend on the noise intensities and correlation time of noise. The first-order and second-order moments are stable when the correlation time of noise is increased. That is, the trichotomous noise plays a constructive role in stabilizing the solution moment with regard to Gaussian white noise. Finally, some numerical results are performed to support the theoretical analyses.