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Study on the Biological Correlation of a Diffusive Food Web Model with Application

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Abstract

Predators possess individual feeding behaviour in their territory. Mostly they attack prey according to their convenience and availability. Sometimes the predator predates upon more than one trophic level for survival. Also, the species go through self-interaction to acquire resources, habitats, food, mates, etc. In this study, we take a food web model consisting of basal prey, intermediate predator, and omnivorous as a top predator. We assume logistic growth for prey and intermediate predator. Here, the prey and the intermediate predator interaction is incorporated by the linear functional response, and other species interactions are followed by Holling Type II. We have studied the temporal as well as the spatio-temporal dynamics of this model. Turing instability conditions are also investigated. We generalize the effect of the diffusion coefficient on the spatial system. Higher-order stability analysis is explained with stability and instability criteria. Numerical verifications with the help of phase portraits, bifurcation, and Turing patterns are presented to illustrate the system’s dynamical behaviour and correlate with the applicability in the real world. We have implicated our model in the agricultural for omnivore carabid species to understand the consequence of their intraspecific interaction as well as trophic interactions. Also, we have validated this correlation with our model dynamics.

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Acknowledgements

This work is supported by ECR Award (File No. ECR/2017/000141), SERB-DST, New Delhi.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Raipur, Chhattisgarh, 492010, India

    S. N. Raw & B. P. Sarangi

  2. Department Of Mathematics, Sharad Chandra Arts Commerce & Science College Naigaon, Nanded, 431709, Maharashtra, India

    A. K. Pandey

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  1. S. N. Raw
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Raw, S.N., Sarangi, B.P. & Pandey, A.K. Study on the Biological Correlation of a Diffusive Food Web Model with Application. Acta Appl Math 181, 16 (2022). https://doi.org/10.1007/s10440-022-00534-6

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