Threshold behavior of a stochastic predator–prey model with fear effect and regime-switching

This work proposes a stochastic predator–prey model with fear effect and regime-switching. It is testified that the dynamical behaviors of the model are determined by two thresholds $F_1$ and $G$: if both $F_1$ and $G$ are positive, then the model admits a unique stationary distribution with the ergodic property; if $F_1$ is positive and $G$ is negative, then the predator population dies out and the prey population is persistent; if $F_1$ is negative, then both the prey population and the predator population die out. Some recent results are improved and extended greatly.