Threshold-driven Bifurcation in a Stochastic Predator-prey System with Mode-switching and Impulsive Effects

A stochastic predator-prey system is developed to investigate the impacts of time-dependent switching, impulsive actions and anti-predator behavior. By the comparison principle and It[Formula: see text] formula, a key threshold [Formula: see text] is theoretically obtained, determining predator persistence or extinction. Based on this, the dynamical bifurcations due to switching and impulses are analyzed. Results reveal that switching may prevent extinction from strong anti-predator behavior but can also cause bifurcations, resulting in either predator persistence or extinction. Appropriate impulses can avoid extinction from switching and boost survival by inducing beneficial bifurcations. However, improper impulses, instead, may decrease population density, intensify population oscillations, and raise the extinction risk. The interaction between switching and impulses emphasizes the significance of coordinated interventions in reducing extinction risks and enhancing ecosystem stability.