Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge

Das, Uttam; Kar, Tapan Kumar; Pahari, U. K.

doi:10.1155/2013/637640

Cited by 9 publications

(5 citation statements)

References 21 publications

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“…Mukherjee [11] investigated a resource according to Holling type I and II functional responses and then showed the effect of constant prey refuge. Das et al [13] described constant prey refuge and harvesting to both predator and prey. Ghosh et al [14] studied the effects of extra food for predator with prey refuge.…”

Section: Jaber and Bahloolmentioning

confidence: 99%

The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

Jabr

Bahlool

2021

eijs

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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 attractors that is a stable point, while periodic dynamics do not exist even on the boundary planes.

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Section: Jaber and Bahloolmentioning

confidence: 99%

The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

Jabr

Bahlool

2021

eijs

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“…Sih [36] investigated the effects of prey refuge and hunting activities. After Das et al [7] examined the effects of refuges' availability on the interaction of predators and prey, Molla et al [21]proposed a mathematical framework for prey-predator enabling prey refuge dependent on each prey and predator species. According to Ko and Ryu's findings in [18], the dynamics of the system integrating a prey refuge with homogenous Neumann boundary conditions are significantly influenced by the configuration of the functional response.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Alternative Resource and Refuge on the Dynamical Behavior of Food Chain Model

Hadi,

Bahlool

2023

MJMS

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This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.

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“…If a population is subjected to a positive extinction rate, then harvesting can drive the population density to a dangerously low level at which extinction becomes sure no matter how the harvest affects the population afterwards. Some works on predator-prey species with harvesting can be found in Das et al [4], Kar et al [5], Clark [6], and Song and Chen [7]. Kar and Pahari [8], Kar and Ghosh [9], and Kumar et al [10] have studied the dynamics in prey-predator models with harvesting and have obtained complex dynamics behavior, such as stability of equilibria, Hopf bifurcation, limit cycle, and heteroclinic bifurcation.…”

Section: Introduction and Model Descriptionmentioning

confidence: 99%

Bifurcation and Feedback Control of an Exploited Prey-Predator System

Das¹

2014

Journal of Chaos

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This paper makes an attempt to highlight a differential algebraic model in order to investigate the dynamical behavior of a prey-predator system due to the variation of economic interest of harvesting. In this regard, it is observed that the model exhibits a singularity induced bifurcation when economic profit is zero. For the purpose of stabilizing the proposed model at the positive equilibrium, a state feedback controller is therefore designed. Finally, some numerical simulations are carried out to show the consistency with theoretical analysis and to illustrate the effectiveness of the proposed controller.

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Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge

Cited by 9 publications

References 21 publications

The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

The Effect of Alternative Resource and Refuge on the Dynamical Behavior of Food Chain Model

Bifurcation and Feedback Control of an Exploited Prey-Predator System

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