The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

Abstract

This paper aims to study the role of a prey refuge that depends on both prey and predator species on the dynamics of a food web model. It is assumed that the food transfer among the web levels occurs according to Lotka-Volterra functional response. The solution properties, such as existence, uniqueness, and uniform boundedness, are discussed. The local, as well as the global, stabilities of the solution of the system are investigated. The persistence of the system is studied with the assistance of average Lyapunov function. The local bifurcation conditions that may occur near the equilibrium points are established. Finally, numerical simulation is used to confirm our obtained results. It is observed that the system has only one type of attractors that is a stable point, while periodic dynamics do not exist even on the boundary planes.

Numerical Analysis of Prey Refuge Effects on the Stability of Holling Type III Four-Species Predator-Prey System

“…The interaction among species is one of these relationships and has been a central subject in mathematical biology due to its pervasiveness and significance [2]. Most scholars (see [3] and [4]), have extensively investigated the qualitative dynamic properties of interacting predator-prey models in order to understand the species' long-term behavior.…”

“…In the modelling of naturally occurring processes, dynamical systems are widely used [3]. The theory of dynamical systems is largely concerned with establishing qualitative predictions about the behavior of systems that evolve over time when the system's control parameters and the initial state change [5].…”

The Effect of Alternative Resource and Refuge on the Dynamical Behavior of Food Chain Model

“…It educates people that every living thing is reliant on other living things for survival. It is crucial to realize that even a small disruption in the natural food chain or feeding habits can cause a large number of species to change their behavior.Jabr and Bahlool [14] have studied the role of a prey refuge, depending on both species, in the dynamics of a food web system. Satar and Naji [34] investigated the stability and bifurcation of a prey-predator-scavenger model in the presence of toxicants and harvesting.…”