In this paper, the effects of prey’s fear on the dynamics of the prey, predator, and scavenger system incorporating a prey refuge with the linear type of functional response were studied theoretically as well as numerically approach. The local and global stabilities of all possible equilibrium points are investigated. The persistence conditions of the model are established. the local bifurcation analysis around the equilibrium points, as well as the Hopf bifurcation near the positive equilibrium point, are discussed and analyzed. Finally, numerical simulations are carried out, and the obtained trajectories are drowned using the application of Matlab version (6) to explain our found analytical

Using a mathematical model to simulate the interaction between prey and predator was suggested and researched. It was believed that the model would entail predator cannibalism and constant refuge in the predator population, while the prey population would experience predation fear and need for a predator-dependent refuge. This study aimed to examine the proposed model's long-term behavior and explore the effects of the model's key parameters. The model's solution was demonstrated to be limited and positive. All potential equilibrium points' existence and stability were tested. When possible, the appropriate Lyapunov function was utilized to demonstrate the equilibrium points' overall stability. The system's persistence requirements were spe

    The relationship between prey and predator populations is hypothesized and examined using a mathematical model. Predation fear, cannibalism among the prey population, and a refuge reliant on predators are predicted to occur. This study set out to look at the long-term behavior of the proposed model and the effects of its key elements. The solution properties of the model were investigated. All potential equilibrium points' existence and stability were looked at. The system's persistence requirements were established. What circumstances could lead to local bifurcation near equilibrium points was uncovered. Suitable Lyapunov functions are used to study the system's overall dynamics. Numerical simulations were conducted to verify the

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 a

We propose an intraguild predation ecological system consisting of a tri-trophic food web with a fear response for the basal prey and a Lotka–Volterra functional response for predation by both a specialist predator (intraguild prey) and a generalist predator (intraguild predator), which we call the superpredator. We prove the positivity, existence, uniqueness, and boundedness of solutions, determine all equilibrium points, prove global stability, determine local bifurcations, and illustrate our results with numerical simulations. An unexpected outcome of the prey's fear of its specialist predator is the potential eradication of the superpredator.

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

     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.

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

An ecological model consisting of prey-predator system involving the prey’s fear is proposed and studied. It is assumed that the predator species consumed the prey according to prey square root type of functional response. The existence, uniqueness and boundedness of the solution are examined. All the possible equilibrium points are determined. The stability analysis of these points is investigated along with the persistence of the system. The local bifurcation analysis is carried out. Finally, this paper is ended with a numerical simulation to understand the global dynamics of the system.