Stability Analysis of a Prey-Predator Model with Prey Refuge and Fear of Adult Predator

Abstract

This paper is concerned with a Holling-II stage-structured predator-prey system in which predators are divided into an immature and mature predators. The aim is to explore the impact of the prey's fear caused by the dread of mature predators in a prey-predator model including intraspecific competitions and prey shelters. The theoretical study includes the local and global stability analysis for the three equilibrium points of the system and shows the prey's fear may lead to improving the stability at the positive equilibrium point. A numerical analysis is given to ensure the accuracy of the theoretical outcomes and to testify the conditions of stability of the system near the non-trivial equilibrium points.

Coprime Factor Model Reduction of Multidimensional Systems

“…There exists a parameter-dependent state-feedback gain 𝐹(𝛿) and 𝑄(𝛿) ∈ 𝑀 that satisfies (9) with (10) for all 𝛿 ∈ 𝛺 if and only if there exists 𝑃(𝛿) ∈ 𝑀, which satisfies:…”

Bifurcation Analysis of an eco-epidemiological model involving prey refuge, fear impact and hunting cooperation

“…discovered and slain by predators [5][6][7][8]. Through these and other studies, researchers have shown how crucial indirect effects like fear are in determining the dynamics between preys and predators.…”

“…Preys' disease and the collaborative hunting efforts of predators can result in heightened fear among prey and an increased likelihood of being captured by predators. Therefore, the presence of prey refuge plays a crucial role in the field of mathematical biology, as it can be viewed as a form of anti-predator behavior that helps safeguard against the extinction of prey populations [1,2,6,8,9,26,27]. In last years, some research papers have proposed models that explore the dynamics between preys and predators, specifically focusing on the presence of diseases within prey species.…”

Dynamical Behavior of Two Predators-One Prey Ecological System with Refuge and Beddington –De Angelis Functional Response

“…given by Lotka-Volterra in 1927 [1], the model was developed by many researchers taking into consideration many factors affecting the system like a refuge in [2,3,4,5,6] and the Beddington-DeAngelis functional response in [6].…”