Stochastic sensitivity analysis and feedback control of noise-induced transitions in a predator-prey model with anti-predator behavior

In this study, we investigate a stochastic predator-prey model with anti-predator behavior. We first analyze the noise-induced transition from a coexistence state to the prey-only equilibrium by using the stochastic sensitive function technique. The critical noise intensity for the occurrence of state switching is estimated by constructing confidence ellipses and confidence bands, respectively, for the coexistence the equilibrium and limit cycle. We then study how to suppress the noise-induced transition by using two different feedback control methods to stabilize the biomass at the attraction region of the coexistence equilibrium and the coexistence limit cycle, respectively. Our research indicates that compared with the prey population, the predators appear more vulnerable and prone to extinction in the presence of environmental noise, but it can be prevented by taking some appropriate feedback control strategies.