Mathematical modeling and analysis of the dynamics of an ecological system with prey refuge and two time delays

Abstract

This paper proposes a prey-predator model with the Hattaf-Yousfi functional response, incorporating a prey refuge and two time delays. Prey refuge is crucial for stabilizing dynamics and preventing the extinction of prey species, as it provides a way for prey to avoid predation. In addition, the paper presents the mathematical analysis of the proposed model and discusses the stability results. Finally, some numerical simulations are given to illustrate the theoretical analysis.