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Intraspecific competition of predator for prey with variable rates in protected areas

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Abstract

In this present study, we systematically explore the periodicity (almost periodic nature) of a dynamical system in time-varying environment, which portrays a special case of prey–predator model governed by non-autonomous differential equations. In particular, we investigate the dynamical characteristics of the underlying prey–predator model by considering modified Leslie–Gower-type model with Crowley–Martin functional response with time-dependent periodic variation of model parameters in a prey reserve area. We show the existence of globally stable periodic solutions. This perpetual prey oscillation results in persistent interference among predator, causing reduced feeding rate at high prey density. A comparative study between the two methods used to prove the existence of periodic (almost periodic) solution of the considered non-autonomous system is also discussed. After showing permanence, existence, uniqueness and global attractivity of the periodic (almost periodic) solution analytically, we demonstrate the typical prey and predator dynamics in time-varying environment using several numerical examples. Partial rank correlation coefficient technique is performed to address how the model output is affected by changes in a specific parameter disregarding the uncertainty over the rest of the parameters.

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Acknowledgements

The research work of first author (Jai Prakash Tripathi) is supported by Science and Engineering Research Board (SERB), India [File No. ECR/2017/002786] and UGC-BSR Research Start-Up-Grant, India [No. F.30-356/2017(BSR)]. The authors are grateful to the handling editor and reviewers for their helpful comments and suggestions that have improved the quality of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Central University of Rajasthan, NH-8, Bandarsindri, Kishangarh, Ajmer, Rajasthan, 305801, India

    Jai Prakash Tripathi

  2. Department of Mathematics and SRM Research Institute, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, 603203, India

    Debaldev Jana & N. S. N. V. K. Vyshnavi Devi

  3. Department of Applied Sciences and Humanities, K.N.I.T., Sultanpur, Uttar Pradesh, 311001, India

    Vandana Tiwari

  4. Gandhi Smarak PG College, Samodhpur, Jaunpur, Uttar Pradesh, 223102, India

    Vandana Tiwari

  5. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, HP, 175005, India

    Syed Abbas

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  1. Jai Prakash Tripathi
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Tripathi, J.P., Jana, D., Vyshnavi Devi, N.S.N.V.K. et al. Intraspecific competition of predator for prey with variable rates in protected areas. Nonlinear Dyn 102, 511–535 (2020). https://doi.org/10.1007/s11071-020-05951-6

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