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Movement, competition and pattern formation in a two prey–one predator food chain model

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Abstract

The complexity of interactions among species remains a captivating phenomenon in the ecology. In this paper, a food chain model characterized by two prey and one predator is analyzed. Unlike previous approaches, our analysis incorporates the velocity of the animals movement into the system, as well as rivalries between prey. We establish a condition for the coexistence of all populations which underscores the importance of the animals’ velocities. Indeed, failing to consider the velocities increases the margin of error in the prediction process. We illustrate various patterns caused by the phenomenon of transport-driven instability.

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Acknowledgements

We would like to express our gratitude to the editor of this manuscript, to Professor Peter Chesson and the reviewers, for their comments.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of South Africa, Johannesburg, 0003, South Africa

    P. M. Tchepmo Djomegni & E. F. Doungmo Goufo

  2. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, University Road, Durban, 4001, South Africa

    K. S. Govinder

  3. Mathematical Biosciences Institute, The Ohio State University, Jennings Hall 3rd Floor, 1735 Neil Ave., Columbus, OH, 43210, USA

    K. S. Govinder

Authors
  1. P. M. Tchepmo Djomegni
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  2. K. S. Govinder
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  3. E. F. Doungmo Goufo
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Correspondence to P. M. Tchepmo Djomegni.

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Communicated by Geraldo Diniz.

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Tchepmo Djomegni, P.M., Govinder, K.S. & Doungmo Goufo, E.F. Movement, competition and pattern formation in a two prey–one predator food chain model. Comp. Appl. Math. 37, 2445–2459 (2018). https://doi.org/10.1007/s40314-017-0459-4

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  • DOI: https://doi.org/10.1007/s40314-017-0459-4

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