Effects of fear and refuge strategy dependent on predator in food web dynamics

Abstract

This study will address a prey and predator model, incorporating a fear coefficient within the prey population. The predator category comprises two distinct types: active predators and scavengers. An assessment will be conducted to examine the influence of refuges on the predator dynamics and the broader system dynamics within the food web. Due to the importance of scavengers for environmental sustainability in waste management, this research was interested in studying the dynamic behavior of the ecosystem consisting of prey-predator-scavengers. Fear of predation, refugees, and harvesting are the biological factors included in the mathematical model to understand their influence on the dynamic behavior of the proposed model. The study comprises a thorough examination of the limitations of solutions, followed by the calculation of equilibrium points. The local and global stability of all points of equilibrium are studied. All the sufficient conditions for the occurrence of local bifurcation are identified. The conditions for the persistence of the model are created. Finally, the numerical solution is utilized to validate our theoretical results and understand the effect of changing parameter values on dynamic behavior. All numerical results were calculated using the Mathematica program. Visual aids, such as diagrams, were employed to enhance clarity in depicting their effects on both predators and the overarching system.