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Complex dynamics of a predator–prey system with fear and memory in the presence of two discrete delays

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Abstract

In this paper, we consider a two-species predator–prey model with fading memory, where the growth rate of prey species is subject to predation induced fear. Growth rate of predator species depends not only on the present density of prey but also on the past densities with diminishing impact. As the societal activities and behavioral practices influence carrying capacity of any species, we consider the density dependent carrying capacity of prey species instead of a constant. As fear on growth rate and societal activities on carrying capacity entail some time lags to show their effect, so we incorporate two delay parameters to corroborate this in the modeling phenomenon. Feasibility criteria of equilibria and their stability analysis are carried out. We observe that fear parameter and predation rate have destabilizing effect on the system’s dynamics, whereas parameter representing intensity of fading memory has stabilizing impact. We also distinguish stability and instability regions in different parametric planes. With increasing value of production factor from negative to positive, stability region decreases. The system also shows multiple stability switching phenomenon with respect to delay parameters. Solutions show chaotic behavior for a range of fear response delay both in the absence and presence of other delay parameter.

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Acknowledgements

The authors are grateful to the anonymous referees for their critical reviews and constructive suggestions that improved the quality and presentation of the paper. Soumitra Pal is thankful to the Council of Scientific and Industrial Research(CSIR), Government of India for providing financial support in the form of senior research fellowship (File.No. 09/013(0915)/2019-EMR-I) and Ashvini Gupta acknowledges the senior research fellowship received from University Grant Commission, New Delhi, India.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, 221005, India

    Soumitra Pal & A. K. Misra

  2. Department of Mathematics, BITS Pilani, Pilani Campus, Pilani, Rajasthan, 333031, India

    Ashvini Gupta & Balram Dubey

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  1. Soumitra Pal
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Correspondence to A. K. Misra.

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Pal, S., Gupta, A., Misra, A.K. et al. Complex dynamics of a predator–prey system with fear and memory in the presence of two discrete delays. Eur. Phys. J. Plus 138, 984 (2023). https://doi.org/10.1140/epjp/s13360-023-04614-w

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