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Competitive exclusion in a two-species chemotaxis model

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Abstract

We consider a mathematical model for the spatio-temporal evolution of two biological species in a competitive situation. Besides diffusing, both species move toward higher concentrations of a chemical substance which is produced by themselves. The resulting system consists of two parabolic equations with Lotka–Volterra-type kinetic terms and chemotactic cross-diffusion, along with an elliptic equation describing the behavior of the chemical. We study the question in how far the phenomenon of competitive exclusion occurs in such a context. We identify parameter regimes for which indeed one of the species dies out asymptotically, whereas the other reaches its carrying capacity in the large time limit.

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Acknowledgments

The second author is partially supported by Ministerio de Economía y Competitividad under grant MTM2009-13655 (Spain) and CCG07-UPM/000-3199 at UPM.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Paderborn, 33098 , Paderborn, Germany

    C. Stinner & M. Winkler

  2. Matemática Aplicada, EU Informática, Universidad Politécnica de Madrid, 28031 , Madrid, Spain

    J. I. Tello

Authors
  1. C. Stinner
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  2. J. I. Tello
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  3. M. Winkler
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Correspondence to J. I. Tello.

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Stinner, C., Tello, J.I. & Winkler, M. Competitive exclusion in a two-species chemotaxis model. J. Math. Biol. 68, 1607–1626 (2014). https://doi.org/10.1007/s00285-013-0681-7

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  • DOI: https://doi.org/10.1007/s00285-013-0681-7

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