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Biological Conservation of a Prey–Predator System Incorporating Constant Prey Refuge Through Provision of Alternative Food to Predators: A Theoretical Study

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Abstract

We describe a prey–predator system incorporating constant prey refuge through provision of alternative food to predators. The proposed model deals with a problem of non-selective harvesting of a prey–predator system in which both the prey and the predator species obey logistic law of growth. The long-run sustainability of an exploited system is discussed through provision of alternative food to predators. We have analyzed the variability of the system in presence of constant prey refuge and examined the stabilizing effect on predator–prey system. The steady states of the system are derived and dynamical behavior of the system is extensively analyzed around steady states. The optimal harvesting policy is formulated and solved with the help of Pontryagin’s maximal principle. Our objective is to maximize the monetary social benefit through protecting the predator species from extinction, keeping the ecological balance. Results finally illustrated with the help of numerical examples.

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Acknowledgments

First author gratefully acknowledges Director, INCOIS for his encouragement and unconditional help. This is INCOIS contribution number 188. The internship work would have been impossible without Joint Science Academies Summer Research Fellowship Programme for 2013. Second author gladly acknowledges Joint Science Academies for providing financial support.

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Authors and Affiliations

  1. Information Services and Ocean Sciences Group, Indian National Centre for Ocean Information Services, Hyderabad “Ocean Valley”, Pragathi Nagar (BO), Nizampet (SO), Hyderabad, 500090, India

    Kunal Chakraborty

  2. Department of Genetics, University of Calcutta, 35 Ballygunge Circular Road, Kolkata, 700019, India

    Sankha Subhra Das

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  1. Kunal Chakraborty
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  2. Sankha Subhra Das
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Correspondence to Kunal Chakraborty.

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Chakraborty, K., Das, S.S. Biological Conservation of a Prey–Predator System Incorporating Constant Prey Refuge Through Provision of Alternative Food to Predators: A Theoretical Study. Acta Biotheor 62, 183–205 (2014). https://doi.org/10.1007/s10441-014-9217-9

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  • DOI: https://doi.org/10.1007/s10441-014-9217-9

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