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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
Wed Dec 15 2021
Journal Name
Abstract And Applied Analysis
Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model
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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

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Publication Date
Tue Feb 27 2024
Journal Name
Mathematical Modelling Of Engineering Problems
Dynamics of a Fractional-Order Prey-Predator Model with Fear Effect and Harvesting
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Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
The Dynamics and Analysis of Stage-Structured Predator-Prey Model Involving Disease and Refuge in Prey Population
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Abstract<p>Start your abstract here the objective of this paper is to study the dynamical behaviour of an eco-epidemiological system. A prey-predator model involving infectious disease with refuge for prey population only, the (SI_) infectious disease is transmitted directly, within the prey species from external sources of the environment as well as, through direct contact between susceptible and infected individuals. Linear type of incidence rate is used to describe the transmission of infectious disease. While Holling type II of functional responses are adopted to describe the predation process of the susceptible and infected predator respectively. This model is represented mathematically by </p> ... Show More
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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 Aug 01 2022
Journal Name
Journal Of Physics: Conference Series
The local bifurcation analysis of two preys stage-structured predator model with anti-predator behavior
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Abstract<p>This paper deals with two preys and stage-structured predator model with anti-predator behavior. Sufficient conditions that ensure the appearance of local and Hopf bifurcation of the system have been achieved, and it’s observed that near the free predator, the free second prey and the free first prey equilibrium points there are transcritical or pitchfork and no saddle node. While near the coexistence equilibrium point there is transcritical, pitchfork and saddle node bifurcation. For the Hopf bifurcation near the coexistence equilibrium point have been studied. Further, numerical analysis has been used to validate the main results.</p>
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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
On The Dynamical Behavior of a Prey-Predator Model With The Effect of Periodic Forcing
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The dynamical behavior of a two-dimensional continuous time dynamical system describing by a prey predator model is investigated. By means of constructing suitable Lyapunov functional, sufficient condition is derived for the global asymptotic stability of the positive equilibrium of the system. The Hopf bifurcation analysis is carried out. The numerical simulations are used to study the effect of periodic forcing in two different parameters. The results of simulations show that the model under the effects of periodic forcing in two different parameters, with or without phase difference, could exhibit chaotic dynamics for realistic and biologically feasible parametric values.

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Publication Date
Mon Jun 05 2023
Journal Name
Communications In Mathematical Biology And Neuroscience
THE DYNAMICS OF A STAGE-STRUCTURE PREY-PREDATOR MODEL WITH HUNTING COOPERATION AND ANTI-PREDATOR BEHAVIOR
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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

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Publication Date
Tue Jan 10 2012
Journal Name
Iraqi Journal Of Science
THE IMPACT OF DISEASE AND HARVESTING ON THE DYNAMICAL BEHAVIOR OF PREY PREDATOR MODEL
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In this paper, a harvested prey-predator model involving infectious disease in prey is considered. The existence, uniqueness and boundedness of the solution are discussed. The stability analysis of all possible equilibrium points are carried out. The persistence conditions of the system are established. The behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that the existence of disease and harvesting can give rise to multiple attractors, including chaos, with variations in critical parameters.

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Publication Date
Sat Apr 01 2023
Journal Name
Journal Of Environmental Accounting And Management
On the Food Chain Model with Sokol Howell Functional Response and Prey Refuge
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The cheif aim of the present investigation is to develop Leslie Gower type three species food chain model with prey refuge. The intra-specific competition among the predators is considered in the proposed model. Besides the logistic growth rate for the prey species, Sokol Howell functional response for predation is chosen for our model formulation. The behaviour of the model system thoroughly analyses near the biologically significant equilibria. The linear stability analysis of the equilibria is carried out in order to examine the response of the system. The present model system experiences Hopf bifurcation depending on the choice of suitable model parameters. Extensive numerical simulation reveals the validity of the proposed model.

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Publication Date
Mon Dec 30 2024
Journal Name
Iraqi Journal Of Science
The Impact of Fear and Anti-Predator Behavior on the Dynamics of Stage-Structure Prey–Predator Model With a Harvesting
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In this paper, an ecological model with stage-structure in prey population, fear, anti-predator and harvesting are suggested. Lotka-Volterra and Holling type II functional responses have been assumed to describe the feeding processes . The local and global stability of steady points of this model are established. Finally, the global dynamics are studied numerically to investigate the influence of the parameters on the solutions of the system, especially the effect of fear and anti-predation.

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