Dynamics of impulsive control in a predator–prey model with the fear effect and group defense

This paper investigates a predator–prey model incorporating both the fear effect and a Holling type Ⅳ functional response with group defense. In this model, the fear effect characterizes the suppression of prey reproduction caused by predator presence, whereas the Holling type Ⅳ functional response describes the enhanced group defense of prey at high densities. First, for the non-impulsive system, we analyze the positivity and boundedness of solutions, as well as the existence and local stability of equilibria. Second, when the equilibrium of the uncontrolled system fails to meet ecological management requirements, we introduce unilateral and bilateral state-feedback impulsive control strategies. The existence of order-one periodic solutions is established by the successor function method, and criteria for orbital asymptotic stability are derived using impulsive Floquet theory. Finally, numerical simulations validate the theoretical results, which provide a theoretical basis for designing ecologically balanced impulsive management strategies that suppress pest outbreaks while maintaining predator and prey populations within acceptable ranges.