@article{Lamrani2023, 
author = {Ilyasse Lamrani and Imad El Harraki and M. A. Aziz-Alaoui and Fatima-Zahrae El Alaoui},
title = {Feedback stabilization for prey predator general model with diffusion via multiplicative controls},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {2360-2385},
keywords = {prey predator with diffusion, Holling responses, feedback stabilization, multiplicative controls, numerical simulations},
url = {https://www.sciopen.com/article/10.3934/math.2023122},
doi = {10.3934/math.2023122},
abstract = {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.}
}