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The role of correlation time in a stochastic population model with density-dependent harvesting

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Abstract

In this paper, a single-species stochastic population model is considered in the presence of density-dependent proportional harvesting. The stochastic model is considered to include the effects of fluctuation in the predation rate and environmental variability. Coloured cross-correlated Gaussian coloured noises are used to generate stochastic fluctuations. Steady-state probability distribution function and stationary potential are determined using the approximate Fokker–Planck equation. Phenomenological bifurcation analysis and mean first passage time have been computed. The average population density in the outbreak state is calculated using normalised probability distribution of the outbreak state. The species outbreak control strategy has been proposed. The key observations of this study are the negative cross-correlation strength-induced noise enhanced stability (NES) phenomenon and the environmental stochasticity-induced resonant activation (RA) phenomenon. Bistable to monostable phase regime shift is observed to depend on the environmental stochasticity whereas monostable to bistatble phase regime shift is observed to depend on correlation time of the environmental stochasticity.

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Acknowledgements

The authors are thankful to the editor and reviewers for critical comments and suggestions, which helped to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Ramkrishna Mahato Government Engineering College, Purulia, 723 103, India

    Saroj Kumar Mandal

  2. Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata, 700 009, India

    Swarup Poria

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  1. Saroj Kumar Mandal
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  2. Swarup Poria
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Correspondence to Swarup Poria.

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Mandal, S.K., Poria, S. The role of correlation time in a stochastic population model with density-dependent harvesting. Pramana - J Phys 97, 69 (2023). https://doi.org/10.1007/s12043-023-02549-6

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  • DOI: https://doi.org/10.1007/s12043-023-02549-6

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