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Stochastics of pattern formation

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Nonlinear Physics of Complex Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 476))

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Abstract

We investigate pattern formation by means of stochastic algorithms. We present three different approaches based on

  1. - i)

    Active Brownian particles

  2. - ii)

    Stochastic cellular automata

  3. - iii)

    master-equation approach

We apply all three algorithms to a simple activator-inhibitor dynamics and show the emergence of spirals, moving and standing spots. The stochastic algorithms during the simulations were very stable and under some conditions faster than the numerical integration of their corresponding mean-field approximations. We also discuss several differences occurring due to the inclusion of fluctuations in the consideration.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Stochastische Prozesse, Institut für Physik, Humboldt-Universität zu Berlin, Invalidenstr. 110, D-10115, Berlin, Germany

    H. Hempel, T. Fricke, M. Mieth & L. Schimansky-Geier

Authors
  1. H. Hempel
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  2. T. Fricke
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  3. M. Mieth
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  4. L. Schimansky-Geier
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Editor information

Jürgen Parisi Stefan C. Müller Walter Zimmermann

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© 1996 Springer-Verlag

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Hempel, H., Fricke, T., Mieth, M., Schimansky-Geier, L. (1996). Stochastics of pattern formation. In: Parisi, J., Müller, S.C., Zimmermann, W. (eds) Nonlinear Physics of Complex Systems. Lecture Notes in Physics, vol 476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105448

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  • DOI: https://doi.org/10.1007/BFb0105448

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61734-1

  • Online ISBN: 978-3-540-70699-1

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