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The Dynamics of Sokol-Howell Prey-Predator Model Involving Strong Allee Effect
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In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

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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
Mon Sep 12 2022
Journal Name
Communications In Mathematical Biology And Neuroscience
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 t

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Publication Date
Wed Aug 10 2022
Journal Name
Mathematics
Modeling and Analysis of the Influence of Fear on the Harvested Modified Leslie–Gower Model Involving Nonlinear Prey Refuge
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Understanding the effects of fear, quadratic fixed effort harvesting, and predator-dependent refuge are essential topics in ecology. Accordingly, a modified Leslie–Gower prey–predator model incorporating these biological factors is mathematically modeled using the Beddington–DeAngelis type of functional response to describe the predation processes. The model’s qualitative features are investigated, including local equilibria stability, permanence, and global stability. Bifurcation analysis is carried out on the temporal model to identify local bifurcations such as transcritical, saddle-node, and Hopf bifurcation. A comprehensive numerical inquiry is carried out using MATLAB to verify the obtained theoretical findings and und

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Publication Date
Sat Jan 01 2022
Journal Name
International Journal Of Differential Equations
Dynamical Behaviours of Stage-Structured Fractional-Order Prey-Predator Model with Crowley-Martin Functional Response
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In this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator.  e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated.  e su‰cient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to con‹rm the theoretical results.

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Publication Date
Tue Feb 13 2024
Journal Name
Iraqi Journal Of Science
Stability Analysis of A stage Structure Prey-Predator Model with Hollimg Type IV Functional Response
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In this paper a stage structure prey-predator model with Hollimg type IV functional response is proposed and analyzed. The local stability analysis of the system is carried out. The occurrence of a simple Hopf bifurcation and local bifurcation are investigated. The global dynamics of the system is investigated with the help of the Lyapunov function. Finally, the analytical obtained results are supported with numerical simulation and the effects of parameters system are discussed. It is observed that, the system has either stable point or periodic dynamics.

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Publication Date
Wed Jun 28 2023
Journal Name
Mathematics
The Impact of Fear on a Harvested Prey–Predator System with Disease in a Prey
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A mathematical eco-epidemiological model consisting of harvested prey–predator system involving fear and disease in the prey population is formulated and studied. The prey population is supposed to be separated into two groups: susceptible and infected. The susceptible prey grows logistically, whereas the infected prey cannot reproduce and instead competes for the environment’s carrying capacity. Furthermore, the disease is transferred through contact from infected to susceptible individuals, and there is no inherited transmission. The existence, positivity, and boundedness of the model’s solution are discussed. The local stability analysis is carried out. The persistence requirements are established. The global behavior of th

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Publication Date
Mon May 11 2020
Journal Name
Baghdad Science Journal
Strong Subordination for E -valent Functions Involving the Operator Generalized Srivastava-Attiya
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Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

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Publication Date
Wed Aug 30 2023
Journal Name
Iraqi Journal Of Science
On the Stability of Four Dimensional Lotka-Volterra Prey-Predator System
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The aim of this work is to study a modified version of the four-dimensional Lotka-Volterra model. In this model, all of the four species grow logistically. This model has at most sixteen possible equilibrium points. Five of them always exist without any restriction on the parameters of the model, while the existence of the other points is subject to the fulfillment of some necessary and sufficient conditions. Eight of the points of equilibrium are unstable and the rest are locally asymptotically stable under certain conditions, In addition, a basin of attraction found for each point that can be asymptotically locally stable. Conditions are provided to ensure that all solutions are bounded. Finally, numerical simulations are given to veri

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Publication Date
Sat Feb 05 2022
Journal Name
Applied Nanoscience
RETRACTED ARTICLE: The impact of fear on a stage structure prey–predator system with anti-predator behavior
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A prey-predator interaction model has been suggested in which the population of a predator consists of a two-stage structure. Modified Holling's disk equation is used to describe the consumption of the prey so that it involves the additional source of food for the predator. The fear function is imposed on prey. It is supposed that the prey exhibits anti-predator behavior and may kill the adult predator due to their struggle against predation. The proposed model is investigated for existence, uniqueness, and boundedness. After determining all feasible equilibrium points, the local stability analyses are performed. In addition, global stability analyses for this model using the Lyapunov method are investigated. The chance of occurrence of loc

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Publication Date
Sat Apr 30 2022
Journal Name
Iraqi Journal Of Science
The Complex Dynamics in a Food Chain Involving Different Functional Responses
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      A food chain model in which the top predator growing logistically has been proposed and studied. Two types of Holling’s functional responses type IV and type II have been used in the first trophic level and second trophic level respectively, in addition to Leslie-Gower in the third level. The properties of the solution are discussed. Since the boundary dynamics are affecting the dynamical behavior of the whole dynamical system, the linearization technique is used to study the stability of the subsystem of the proposed model. The persistence conditions of the obtained subsystem of the food chain are established. Finally, the model is simulated numerically to understand the global dynamics of the food chain un

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