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Huang et al. [1] recently developed a toxin-dependent predator-prey model and analyzed its global dynamics. Their results showed that environmental toxins may influence both predators and prey and induce bistable situation, and intermediate toxin concentrations may affect predators disproportionately through biomagnification. Environmental noises can change the dynamical behaviors of the toxin-based predator-prey model. In this paper, by formulating a stochastically forced predator-prey model with environmental toxins, we study the dynamical phenomenon of noise-induced transitions from coexistence to prey-only extirpation in the bistable zone. Numerical simulations based on the technique of stochastic sensitivity functions are provided for constructing the confidence ellipse and estimating the threshold value of the noise intensity of state switching. Meanwhile, we construct the confidence band and study the configurational arrangement of the stochastic cycle.

Stochastic sensitivity analysis of noise-induced transitions in a predator-prey model with environmental toxins