The food web is a crucial conceptual tool for understanding the dynamics of energy transfer in an ecosystem, as well as the feeding relationships among species within a community. It also reveals species interactions and community structure. As a result, an ecological food web system with two predators competing for prey while experiencing fear was developed and studied. The properties of the solution of the system were determined, and all potential equilibrium points were identified. The dynamic behavior in their immediate surroundings was examined both locally and globally. The system’s persistence demands were calculated, and all conceivable forms of local bifurcations were investigated. With the aid of MATLAB, a numerical simu

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

The aim of this study is to utilize the behavior of a mathematical model consisting of three-species with Lotka Volterra functional response with incorporating of fear and hunting cooperation factors with both juvenile and adult predators. The existence of equilibrium points of the system was discussed the conditions with variables. The behavior of model referred by local stability in nearness of any an equilibrium point and the conditions for the method of approximating the solution has been studied locally. We define a suitable Lyapunov function that covers every element of the nonlinear system and illustrate that it works. The effect of the death factor was observed in some periods, leading to non-stability. To confirm the theore

It is recognized that organisms live and interact in groups, exposing them to various elements like disease, fear, hunting cooperation, and others. As a result, in this paper, we adopted the construction of a mathematical model that describes the interaction of the prey with the predator when there is an infectious disease, as well as the predator community's characteristic of cooperation in hunting, which generates great fear in the prey community. Furthermore, the presence of an incubation period for the disease provides a delay in disease transmission from diseased predators to healthy predators. This research aims to examine the proposed mathematical model's solution behavior to better understand these elements' impact on an eco-epidemi

A harvested prey-predator model with infectious disease in preyis investigated. It is assumed that the predator feeds on the infected prey only according to Holling type-II functional response. The existence, uniqueness and boundedness of the solution of the model are investigated. The local stability analysis of the harvested prey-predator model is carried out. The necessary and sufficient conditions for the persistence of the model are also obtained. Finally, the global dynamics of this model is investigated analytically as well as numerically. It is observed that, the model have different types of dynamical behaviors including chaos.

The mathematical construction of an ecological model with a prey-predator relationship was done. It presumed that the prey consisted of a stage structure of juveniles and adults. While the adult prey species had the power to fight off the predator, the predator, and juvenile prey worked together to hunt them. Additionally, the effect of the harvest was considered on the prey. All the solution’s properties were discussed. All potential equilibrium points' local stability was tested. The prerequisites for persistence were established. Global stability was investigated using Lyapunov methods. It was found that the system underwent a saddle-node bifurcation near the coexistence equilibrium point while exhibiting a transcritical bifurcation

Global warming has a serious impact on the survival of organisms. Very few studies have considered the effect of global warming as a mathematical model. The effect of global warming on the carrying capacity of prey and predators has not been studied before. In this article, an ecological model describing the relationship between prey and predator and the effect of global warming on the carrying capacity of prey was studied. Moreover, the wind speed was considered an influencing factor in the predation process after developing the function that describes it. From a biological perspective, the nonnegativity and uniform bounded of all solutions for the model are proven. The existence of equilibria for the model and its local stability is inves

Taking into account the significance of food chains in the environment, it demonstrates the interdependence of all living things and has economic implications for people. Hunting cooperation, fear, and intraspecific competition are all included in a food chain model that has been developed and researched. The study tries to comprehend how these elements affect the behavior of species along the food chain. We first examined the suggested model's solution properties before calculating every potential equilibrium point and examining the stability and bifurcation nearby. We have identified the factors that guarantee the global stability of the positive equilibrium point using the geometric approach. Additionally, the circumstances that would gu

In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynami