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Stability analysis of Turing patterns generated by the Schnakenberg model

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Abstract.

We consider the following Schnakenberg model on the interval (-1,1): where We rigorously show that the stability of symmetric N-peaked steady-states can be reduced to computing two matrices in terms of the diffusion coefficients D1, D2 and the number N of peaks. These matrices and their spectra are calculated explicitly and sharp conditions for linear stability are derived. The results are verified by some numerical simulations.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Irvine, Irvine, CA 92697-3875, USA

    David Iron

  2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

    Juncheng Wei

  3. Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany

    Matthias Winter

Authors
  1. David Iron
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  2. Juncheng Wei
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  3. Matthias Winter
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Correspondence to Matthias Winter.

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Mathamatics Subject Classification (2000): Primary 35B40, 35B45; Secondary 35J55, 92C15, 92C40

Revised version: 10 October 2003

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Iron, D., Wei, J. & Winter, M. Stability analysis of Turing patterns generated by the Schnakenberg model. J. Math. Biol. 49, 358–390 (2004). https://doi.org/10.1007/s00285-003-0258-y

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