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2006-TK_Kar-Controllability and optimal harvesting of a prey–predator model incorporating a prey refuge

Author(s): Tapan Kumar Kar

NA

Keywords: survival predator-prey harvest refuge Pontryagin’s maximal principle hiding optimal harvest

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Abstract

Resource Image This paper deals with a prey–predator model incorporating a prey refuge and harvesting of the predator species.

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Kar, Tapan Kumar.  2006: Controllability and optimal harvesting of a prey–predator model incorporating a prey refuge.  International Journal of Mathematical Education in Science and Technology. 37(5): 559-571.

See https://www.tandfonline.com/doi/abs/10.1080/00207390600598011 . Accessed on 27 March 2023.

Abstract: This paper deals with a prey–predator model incorporating a prey refuge and harvesting of the predator species. A mathematical analysis shows that prey refuge plays a crucial role for the survival of the species and that the harvesting effort on the predator may be used as a control to prevent the cyclic behaviour of the system. The optimal harvest policy is studied, and the solution is derived in the equilibrium case by using Pontryagin’s maximal principle. Some numerical simulations are taken to illustrate the established results.

This paper deals with a qualitative approach with attention to equilibrium values and stability.

 Keywords: differential equation, population, model, predator prey model, refuge, hiding, stability

 

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Author(s): Tapan Kumar Kar

NA

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