Threshold behavior of a stochastic predator-prey system with prey refuge and fear effect

Abstract In this paper, we investigate the threshold behavior of a stochastic predator–prey system with prey refuge, fear effect and non-constant mortality rate. First, we obtain thresholds which can determine the extinction and persistence in the mean of prey and predator. Then we establish the threshold for the existence of a unique ergodic stationary distribution via constructing suitable Lyapunov functions. We can draw conclusions: (1) the survival rate of prey can be improved by increasing the strength of refuge, decreasing the cost of fear or reducing the intensity of white noise; (2) the survival rate of predator can be improved by weakening the strength of refuge, increasing the cost of fear or reducing the intensity of white noise.

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