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.
Highlights
Mathematical modeling is used to understand the interaction of organisms with their surrounding environment, as well as species evolution that is well-known biological evolution
It is completely recognized that a prey-predator is fundamental interaction for drawing the dynamics of food webs in the real-world environment, predation risks can negatively affect prey biomass and growth efficiency, and predators affect the structure of natural communities
Using condition (59f), it is observed that ðdL3/dtÞ < 0, which means that L3 is a Lyapunov function and the generalist-predator free equilibrium point (GPFP) is an A.S for any trajectory starting from a point that belongs to the region that satisfies the above conditions
Summary
Mathematical modeling is used to understand the interaction of organisms with their surrounding environment, as well as species evolution that is well-known biological evolution. Kumar and Kumari [9] discussed the action of fear on the dynamics of the food chain model having three species. They obtained that for low fear’s scale, the system stays chaotic while relatively high fear’s scale leads to stability. Singh and Bhadauria [14] studied the dynamics of the prey-predator model with weak Allee effect II and modified Leslie-Gower. They explained that Allee effect II greatly impacts the model and can raise the risk of extinction.
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