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. [ABSTRACT FROM AUTHOR]