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Analysis of a harvested predator–prey system with schooling behaviour

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Abstract

In this paper, we have considered a predator–prey fishery model under harvesting, where the prey exhibits schooling behaviour. Positivity and boundedness of the system are discussed. Some criteria for the extinction of prey and predator populations are derived. Stability analysis of the equilibrium points are presented. Some criteria for Hopf bifurcation are derived. The optimal harvest policy is also discussed using Pontryagin’s Maximum Principle, where the effort is used as the control parameter to protect fish population from overfishing. Numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically.

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Acknowledgements

The authors are grateful to the anonymous referees and Professor Jian-Qiao Sun (Editor-in-Chief) for their careful reading, valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly.

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Authors and Affiliations

  1. Department of Mathematics, Surendranath Evening College, Kolkata, 700009, India

    Debasis Manna

  2. Department of Mathematics, Vidyasagar Evening College, Kolkata, 700006, India

    Alakes Maiti

  3. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India

    G. P. Samanta

Authors
  1. Debasis Manna
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  2. Alakes Maiti
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  3. G. P. Samanta
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Correspondence to Debasis Manna.

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Manna, D., Maiti, A. & Samanta, G.P. Analysis of a harvested predator–prey system with schooling behaviour. Int. J. Dynam. Control 6, 881–891 (2018). https://doi.org/10.1007/s40435-017-0321-y

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  • DOI: https://doi.org/10.1007/s40435-017-0321-y

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