The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear

Abstract

The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels. It is assumed that the generalist predator grows logistically using the Leslie-Gower type of growth function. All the solution properties of the model are studied. Local dynamics behaviors are investigated. The basin of attraction for each equilibrium is determined using the Lyapunov function. The conditions of persistence of the model are specified. The study of local bifurcation in the model is done. Numerical simulations are implemented to show the obtained results. It is watched that the system is wealthy in its dynamics including chaos. The fear factor works as a stabilizing factor in the system up to a specific level; otherwise, it leads to the extinction of the predator. However, increasing the prey’s group defense leads to extinction in predator species.

Fear and Hunting Cooperation's Impact on the Eco-Epidemiological Model's Dynamics

“…However, the presence of a predator may drastically alter the prey's physiological and behavioral characteristics to the point where it may have a greater impact on the prey population than direct predation [17] and the mentioned references therein. There are many research studies using mathematical modeling considered the impact of hunting cooperation [1,[17][18][19][20][21][22][23][24][25] and the impact of fear [16,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] in the prey-predator models separately. Numerous prey species alter their behavior when predators are around because of the possibility of being eaten.…”

Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model

“…They demonstrated that prey-predator interactions can be stabilized by significant anti-predator reflexes. With fear, Maghool et al 14 built and investigated a tritrophic Leslie-Gower food-web system. Because of the prey group's protective capability, the Sokol-Howell type of function response is employed to describe the predation process.…”

The Impact of Fear on a Harvested Prey–Predator System with Disease in a Prey

“…In contrast, in the indirect example, a predator's presence drastically alters the prey's behavior due to their dread of the threat of predation [30]. As a result, numerous studies have been conducted to comprehend how prey fear affects the dynamics of the prey-predator system, see [9,[31][32][33][34][35][36][37][38][39] and the references therein. Despite the aforementioned, this paper combines the effects of fear, disease, and harvest in a single prey-predator system.…”