Abstract:The stability of a Harrison predator-prey model driven by symmetric trichotomous noises is studied in this paper. Using the ShapiroLoginov formula, the firstorder and secondorder moments of the linearized system are obtained. Then, the stability condition of the Harrison predator-prey model is given by using RouthHurwitz stability criterion. It is found that the stability of the system depends on the noise intensities and correlation time. Finally, some numerical results are performed to support the theoretical analyses.