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Explicit impacts of harvesting on a fractional-order delayed predator–prey model

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Abstract

We propose a fractional-order prey-predator model with delay and harvesting. Comparatively, only a few analyses are made to explore the impact of harvesting on population fluctuation due to time delay and fractional order. Thus, our focus is whether harvesting effort can stabilize or destabilize the system by varying the fractional order or keeping it fixed. We have observed that fractional order influences the delayed system and the number of stability switching differently in the case of either predator or prey harvesting. Both fractional order and predator harvesting have a destabilizing effect, whereas prey harvesting has a stabilizing effect on the system. In addition, we observed stability switching induced by predator harvesting while keeping the delay fixed. Moreover, in the case of predator harvesting, when the carrying capacity of prey exceeds a certain threshold, the number of switching regions increases significantly. For yield maximization, we observe that maximum sustainable yield (MSY) exists for predator harvesting only; however, yield at MSY produces stable stock only when the time delay is minimal.

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Data availability statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: During this study, no datasets were created or analyzed].

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Acknowledgements

The research work of Bidhan Bhunia is financially supported by UGC-NFSC, India(Ref. No.:191620076432), and the research work of Lakpa Thendup Bhutia is financially supported by Council of Scientific and Industrial Research (CSIR), India (File No. 08/0003(13400)/2022-EMR-I, dated: 4th March 2022).

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal, 711103, India

    Bidhan Bhunia, Lakpa Thendup Bhutia & Tapan Kumar Kar

  2. Department of Basic Science and Humanities, Techno International New Town Rajarhat, Kolkata, West Bengal, 700156, India

    Papiya Debnath

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  1. Bidhan Bhunia
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Contributions

This manuscript is prepared by Bidhan Bhunia, Lakpa Thendup Bhutia, Tapan Kumar Kar, and Papiya Debnath. Bidhan Bhunia and Lakpa Thendup Bhutia have a main role in designing the approach and performing the analysis and writing the manuscript, with substantial input from Tapan Kumar Kar and Papiya Debnath.

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Correspondence to Bidhan Bhunia.

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Bhunia, B., Bhutia, L.T., Kar, T.K. et al. Explicit impacts of harvesting on a fractional-order delayed predator–prey model. Eur. Phys. J. Spec. Top. 232, 2629–2644 (2023). https://doi.org/10.1140/epjs/s11734-023-00941-2

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