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

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.