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Studies of dynamical behaviours of an imprecise predator-prey model with Holling type II functional response under interval uncertainty

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Abstract

Our goal in this paper is to examine an imprecise predator-prey model in an interval environment. The present imprecise model is constructed, in part, by modifications to the Lotka–Volterra model with appropriate biology parameters taken as intervals. The Holling type II functional response is considered instead of the Holling Type I functional response, along with the predators’ interaction with themselves. Using a linear parametric representation of the interval, we can represent the imprecise model in a parametric form precisely. Next, we analyse the mathematical properties of the proposed model, like finding equilibrium with various stability conditions and investigating several bifurcations of the system. The justifications of all analytical results for our system are illustrated numerically with the interval-valued data of parameters, and the simulated results are express graphically. Finally, we conclude our work with suggestions and analyse the biological significance of our findings through numerical evaluations.

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Acknowledgements

The authors would want to thank anonymous reviewers and Editor for their valuable comments and constructive suggestions for improving this manuscript. The First author Bapin Mondal would like to thank UGC (Fellowship ID-1152/CSIR-UGC NET DEC 2018), Government of India, New Delhi.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Calcutta, Kolkata, 700009, India

    Bapin Mondal, Susmita Sarkar & Uttam Ghosh

  2. Department of Mathematics, The University of Burdwan, Burdwan, 713104, India

    Md Sadikur Rahman

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  1. Bapin Mondal
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  4. Uttam Ghosh
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Mondal, B., Rahman, M.S., Sarkar, S. et al. Studies of dynamical behaviours of an imprecise predator-prey model with Holling type II functional response under interval uncertainty. Eur. Phys. J. Plus 137, 74 (2022). https://doi.org/10.1140/epjp/s13360-021-02308-9

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