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Analysis of a predator-prey model for exploited fish populations with schooling behavior

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  • Manna, Debasis
  • Maiti, Alakes
  • Samanta, G.P.

Abstract

In this paper, a predator-prey model for exploited fish populations is considered, where the prey and the predator both show schooling behavior. Due to this coordinated behavior, predator-prey interaction occurs only at the outer edge of the schools formed by the populations. Positivity and boundedness of the model are discussed. Analysis of the equilibria is presented. A criterion for Hopf bifurcation is obtained. The optimal harvest policy is also discussed using Pontryagin’s maximum principle, where the effort is used as the control parameter. Numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically.

Suggested Citation

  • Manna, Debasis & Maiti, Alakes & Samanta, G.P., 2018. "Analysis of a predator-prey model for exploited fish populations with schooling behavior," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 35-48.
    • Handle: RePEc:eee:apmaco:v:317:y:2018:i:c:p:35-48
    DOI: 10.1016/j.amc.2017.08.052
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    References listed on IDEAS

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    1. Marzano, Annalisa, 2013. "Harvesting the Sea: The Exploitation of Marine Resources in the Roman Mediterranean," OUP Catalogue, Oxford University Press, number 9780199675623, Decembrie.
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    Cited by:

    1. Shang, Lihui & Xu, Zhiqiang, 2023. "Adaptive control strategy improves synchronization of self-propelled agents," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    2. Das, Amartya & Samanta, G.P., 2020. "A prey–predator model with refuge for prey and additional food for predator in a fluctuating environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    3. Das, Amartya & Samanta, G.P., 2018. "Stochastic prey–predator model with additional food for predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 121-141.
    4. You, Feng & Yang, Han-Xin & Li, Yumeng & Du, Wenbo & Wang, Gang, 2023. "A modified Vicsek model based on the evolutionary game," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    5. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Three-dimensional pattern dynamics of a fractional predator-prey model with cross-diffusion and herd behavior," Applied Mathematics and Computation, Elsevier, vol. 421(C).

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