Sustainability and optimal control of an exploited prey predator system through provision of alternative food to predator

Kar, Tapan Kumar; Ghosh, Bapan

doi:10.1016/j.biosystems.2012.02.003

Cited by 70 publications

(22 citation statements)

References 17 publications

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“…Economic interest motivates the introduction of harvesting in the prey-predator models. There are many studies, which show that the harvesting effort has effect on the system dynamic, and get the optimal strategy [24][25][26] . In this paper, we discuss the influence of the harvesting effort on the system with Holling type-IV by using the theoretical analysis and numerical simulations.…”

Section: Discussionmentioning

confidence: 99%

Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation

Zhang¹,

Wang²,

Qin³

2015

ACM

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This paper deals with a discrete-time prey-predator system with Holling type-IV function response in the presence of some alternative food to predator and harvesting of prey species. By theoretical analysis and numerical simulation, comparing with the system without harvesting, ecological equilibrium point of the system is removed if harvesting effort is changed, and the appropriate harvesting effort can increase the stability of the system. Moreover, optimal harvesting policy is obtained using Pontryagin's maximum principle. Meanwhile, some numerical simulations verify our analytical results. This study also gains the maximum economic profit which is based on the ecological equilibrium. The suitable price of resources can control the excessive harvest to promote the sustainable development of species.

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Section: Discussionmentioning

confidence: 99%

Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation

Zhang¹,

Wang²,

Qin³

2015

ACM

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“…< ε (see [20]); otherwise update the control using a convex combination of the current and previous control and GO to step 2. Here, x i is the ith iterative solution of the state system and ε is an arbitrarily small positive quantity.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

An optimal control problem for ovine brucellosis with culling

Nannyonga

Mwanga

Luboobi

2015

Journal of Biological Dynamics

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“…Exploitation reduces the biomass of the concerned species, exhibits oscillation, and even causes extinction of some other species. Rosenweig-MacAurtho model experiences oscillation under selective effort of Kar and Ghosh [2]. Legovic et al [3] have concluded that harvesting the prey species at maximum level causes the extinction of the predator species in traditional prey-predator system.…”

Section: Introduction and Model Descriptionmentioning

confidence: 99%

Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting

Das

Kar

2014

Journal of Nonlinear Dynamics

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This paper tries to highlight a delayed prey-predator model with Holling type III functional response and harvesting to predator species. In this context, we have discussed local stability of the equilibria, and the occurrence of Hopf bifurcation of the system is examined by considering the harvesting effort as bifurcation parameter along with the influences of harvesting effort of the system when time delay is zero. Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by applying the normal form theory and the center manifold theorem. Lastly some numerical simulations are carried out to draw for the validity of the theoretical results.

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Sustainability and optimal control of an exploited prey predator system through provision of alternative food to predator

Cited by 70 publications

References 17 publications

Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation

Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation

An optimal control problem for ovine brucellosis with culling

Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting

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