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In a predator-prey interaction, there are many factors present which affectthe growth of the species, either positively or negatively. Fear of predationis such a factor which causes psychological stress in a prey species so thattheir overall growth starts to reduce. In this work, a predator-prey model isproposed where the prey species is facing such reduction in their growth out offear, and also the predator is provided with an alternative food source whichhelps the prey to hide themselves in a safe place meanwhile. The dynamicsproduces a wide range of interesting results, including the significance of thepresence of a certain amount of fear or even prey refuge for populationcoexistence. The analysis is extended later to the nonlocal model to analyzehow the non-equilibrium phenomena influence the dynamical behaviour. It isobserved through numerical simulations that though the scope of patternformation reduces with the increase of fear level in the spatio-temporal model,but the incorporation of nonlocal interaction further increases the chance ofspecies colonization.

The analysis of the impact of fear in the presence of additional food and prey refuge with nonlocal predator-prey models