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Transient indicator of exploited communities at equilibrium in generalist predator–prey models

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Abstract

Most research articles on the exploited predator–prey dynamics study the asymptotic profile of steady states, bistability, limit cycles and bifurcations. In these cases, the disturbances (harvesting) can lead to transient amplification before decaying asymptotically. Therefore, a deep understanding of transient dynamics near steady state is crucial to guessing the dynamics of interacting species for disturbances on short time scales. Here, we study this transient indicator to a generalist predator–prey system with Holling type III functional response. The disturbances are produced by different harvesting strategies, including prey harvesting, predator harvesting, and simultaneous harvesting of both species. In the case of the existence of unique interior equilibrium, the stable steady state becomes reactive. The results become complicated when the system becomes bistable in nature. Between two stable coexistence states, one becomes reactive, and another remains non-reactive. But it is observed that disturbance made by harvesting in our system affects the transient behavior of the system making it more stable in nature in every case compared to the unharvested system. We also observe that the MSY policy is suitable for prey and simultaneous harvesting of both species in comparison with predator harvesting.

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Data Availability Statement

No data are associated with the manuscript.

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Acknowledgements

The work by Esita Das is financially supported by the Indian Institute of Engineering Science and Technology (IIEST), Shibpur, India (No. 1999/Exam, dated: October 01, 2021). The research of T.K. Kar is supported by the Council of Scientific and Industrial Research (CSIR) (NO.25(0300)/19/EMR-II, dated: May 16, 2019).

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Authors and Affiliations

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

    Esita Das & T. K. Kar

  2. Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India

    Prosenjit Paul

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This manuscript is prepared by Esita Das, Prosenjit Paul and T.K. Kar; Esita Das and Prosenjit Paul have taken the main role in designing the approach and performed the analysis and writing of the manuscript, with substantial input from T.K. Kar.

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Correspondence to Esita Das.

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Das, E., Paul, P. & Kar, T.K. Transient indicator of exploited communities at equilibrium in generalist predator–prey models. Eur. Phys. J. Plus 137, 1221 (2022). https://doi.org/10.1140/epjp/s13360-022-03429-5

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