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The influence of fear on the dynamic of an eco-epidemiological system with predator subject to the weak Allee effect and harvesting
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In this paper, an eco-epidemiological prey-predator system when the predator is subjected to the weak Allee effect, and harvesting was proposed and studied. The set of ordinary differential equations that simulate the system’s dynamic is constructed. The impact of fear and Allee’s effect on the system's dynamic behavior is one of our main objectives. The properties of the solution of the system were studied. All possible equilibrium points were determined, and their local, as well as global stabilities, were investigated. The possibility of the occurrence of local bifurcation was studied. Numerical simulation was used to further evaluate the global dynamics and understood the effects of varying parameters on the asymptotic behavior of the system. It is observed that the system has different types of attractors including stable point, periodic, and even bi-stable behavior.

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Publication Date
Sat Oct 15 2022
Journal Name
Communications In Mathematical Biology And Neuroscience
Modeling and analysis of a prey-predator system incorporating fear, predator-dependent refuge, and cannibalism
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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

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Publication Date
Fri Aug 30 2024
Journal Name
Iraqi Journal Of Science
The Migration Effect on an Eco-toxicant Model
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This paper proposes and studies an ecotoxicant system with Lotka-Volterra functional response for predation including prey protective region. The equilibrium points and the stability of this model have been investigated analytically both locally and globally. Finally, numerical simulations and graphical representations have been utilized to support our analytical findings

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Publication Date
Fri Nov 01 2019
Journal Name
Journal Of Physics: Conference Series
The Bifurcation analysis of Prey-Predator Model in The Presence of Stage Structured with Harvesting and Toxicity
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Abstract<p>For a mathematical model the local bifurcation like pitchfork, transcritical and saddle node occurrence condition is defined in this paper. With the existing of toxicity and harvesting in predator and prey it consist of stage-structured. Near the positive equilibrium point of mathematical model on the Hopf bifurcation with particular emphasis it established. Near the equilibrium point E<sub>0</sub> the transcritical bifurcation occurs it is described with analysis. And it shown that at equilibrium points E<sub>1</sub> and E<sub>2</sub> happened the occurrence of saddle-node bifurcation. At each point the pitch fork bifurcation occurrence is not happened. </p> ... Show More
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Publication Date
Wed Jan 02 2019
Journal Name
Differential Equations And Dynamical Systems
Stability and Bifurcation in a Prey–Predator–Scavenger System with Michaelis–Menten Type of Harvesting Function
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Publication Date
Mon Apr 04 2022
Journal Name
Communications In Mathematical Biology And Neuroscience
Stability and bifurcation of a prey-predator system incorporating fear and refuge
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It is proposed and studied a prey-predator system with a Holling type II functional response that merges predation fear with a predator-dependent prey's refuge. Understanding the impact of fear and refuge on the system's dynamic behavior is one of the objectives. All conceivable steady-states are investigated for their stability. The persistence condition of the system has been established. Local bifurcation analysis is performed in the Sotomayor sense. Extensive numerical simulation with varied parameters was used to explore the system's global dynamics. A limit cycle and a point attractor are the two types of attractors in the system. It's also interesting to note that the system exhibits bi-stability between these 2 types of attractors.

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Publication Date
Mon Nov 11 2024
Journal Name
International Journal Of Dynamics And Control
The modified predator–prey model response to the effects of global warming, wind flow, fear, and hunting cooperation
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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

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Publication Date
Wed Sep 01 2021
Journal Name
Journal Of Applied Mathematics
The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear
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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

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Publication Date
Wed May 14 2025
Journal Name
Journal Of Applied Mathematics
Role of Wind and Fear on the Dynamic of a Prey and Two Competing Predators
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An essential tool for studying the web is its ability to show how energy moves through an ecosystem. Understanding and elucidating the relationship between species variety and their placement within the inclusive trophic dynamics is also beneficial. A food web ecological model with prey and two rival predators under fear and wind flow conditions is developed in this article. The boundedness and positivity of the system’s solution are established mathematically. The stability and existence constraints of the system’s equilibria are examined. The proposed system’s persistence limitations are established. Additionally, the bifurcation analysis of every potential equilibrium is examined using the Sotomayor theorem. To describe the

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Publication Date
Tue Dec 24 2024
Journal Name
Malaysian Journal Of Mathematical Sciences
Exploring the Role of Hunting Cooperation, and Fear in a Prey-Predator Model with Two Age Stages
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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

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Publication Date
Sun Oct 01 2023
Journal Name
Baghdad Science Journal
Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model
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A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify the va

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