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A comparative study of bioeconomic ratio-dependent predator–prey model with and without additional food to predators

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Abstract

We present two models which incorporate prey harvesting to the classical and a modified ratio-dependent predator–prey model with additional food supply to the predators. We analyze the existence and stability of the equilibrium points of both the models and determine the maximum sustainable harvesting effort. The optimal harvesting policy is determined by using Pontryagin’s maximum principle. The results obtained are numerically illustrated. We examine the consequences of providing additional food (as a part of the total harvest effort) to predators in prey harvesting. Our study shows that the system can sustain a much improved optimal prey harvesting rate with additional food supply.

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Acknowledgments

The first author is grateful to the Indian Institute of Technology Guwahati for the financial support provided to pursue his Ph.D. The authors express their gratitude to both the learned reviewers for their suggestions, which resulted in an improved manuscript.

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  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India

    Dinesh Kumar & Siddhartha P. Chakrabarty

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  1. Dinesh Kumar
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  2. Siddhartha P. Chakrabarty
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Correspondence to Siddhartha P. Chakrabarty.

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Kumar, D., Chakrabarty, S.P. A comparative study of bioeconomic ratio-dependent predator–prey model with and without additional food to predators. Nonlinear Dyn 80, 23–38 (2015). https://doi.org/10.1007/s11071-014-1848-5

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  • DOI: https://doi.org/10.1007/s11071-014-1848-5

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