Feedback stabilization for prey predator general model with diffusion via multiplicative controls

In this paper, we consider a predator–prey model given by a reaction–diffusion system. This model encompasses the classic Holling Ⅰ, Holling Ⅱ, Holling Ⅲ, and Holling Ⅳ functional responses. We investigate the stabilization problem of the considered system using multiplicative controls. By linearizing the system and using the maximum principle, we construct a multiplicative control that exponentially stabilizes the system towards its steady-state solutions. The proposed feedback control allows us to reach a large class of steady-state solutions. The global well-posedness is obtained via Banach fixed point. Applications and numerical simulations to Holling responses Ⅰ, Ⅱ, Ⅲ, and Ⅳ are presented.