Effects of fear and anti-predator response in a discrete system with delay

Abstract

<p style='text-indent:20px;'>In this paper a discrete-time two prey one predator model is considered with delay and Holling Type-Ⅲ functional response. The cost of fear of predation and the effect of anti-predator behavior of the prey is incorporated in the model, coupled with inter-specific competition among the prey species and intra-specific competition within the predator. The conditions for existence of the equilibrium points are obtained. We further derive the sufficient conditions for permanence and global stability of the co-existence equilibrium point. It is observed that the effect of fear induces stability in the system by eliminating the periodic solutions. On the other hand the effect of anti-predator behavior plays a major role in de-stabilizing the system by giving rise to predator-prey oscillations. Finally, several numerical simulations are performed which support our analytical findings.</p>

Fear and Group Defense Effect of a Holling Type IV Predator-Prey System Intraspecific Competition

“…Predatory characteristics determine the formation of the predation function in the dynamic model. The Holling function response is representative and realistic for the predation function [27]. The first predation response function is Holling Type I, characterized by a monotonically increasing predation function.…”

Impact of Fear Behavior on Prey Population Growth Prey-Predator Interaction

“…The formulation of a mathematical model on prey will be developed in the form of a function with a fear effect based on the assumptions that have been given [23]. The function with the fear effect will be given on the growth of the prey species by multiplying the form 𝑓(𝛼, 𝛽, 𝑦), so that the form model (1) becomes…”

“…Mathematical model of the population using the well-known logistic growth first considers a linear birth rate. The Lotka-Volterra population growth model introduces logistical types of population growth for prey and various types of response functions that represent a realistic interplay between prey and predators [1].…”