Combined effects of prey refuge and death rate of predator on the prey-predator population dynamics

The study of population dynamics involving prey-predator interactions has received significant attention in ecology due to the influential role that biotic interactions (i.e., interactions between species) has played in the development of ecological theory. One way to understand this role is by using mathematical models. To address this problem, we employ a Rosenzweig-MacArthur prey-predator model incorporating a prey refuge. We examine the existence and stability of different steady states in this model, which correspond to different possible outcomes of species interactions. We also investigate the combined influences of prey refuge and the death rate of predator on species population dynamics. In particular, we observe the occurrence of different bifurcations in this model, which can shape the overall dynamics of the system. These threshold phenomena determine the conditions under which different outcomes of species interactions e.g., species coexistence, species extinction and oscillatory dynamics occur as the strength of some ecologically-relevant parameters change.