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Turing Patterns in Deserts

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How the World Computes (CiE 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7318))

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Abstract

Self-organised patterns of vegetation are a characteristic feature of many semi-arid regions. In particular, banded vegetation is typical on hillsides. Mathematical modelling is widely used to study these banded patterns, because there are no laboratory replicates. I will describe the development of spatial patterns in an established model for banded vegetation via a Turing bifurcation. I will discuss numerical simulations of the phenomenon, and I will summarise nonlinear analysis on the existence and form of spatial patterns as a function of the model parameter that corresponds to mean annual rainfall.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom

    Jonathan A. Sherratt

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  1. Jonathan A. Sherratt
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Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Computer Laboratory, University of Cambridge, Willialm Gates Building, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  3. Institute for Logic, Language and Computation, University of Amsterdam, 1090 GE, Amsterdam, The Netherlands

    Benedikt Löwe

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Sherratt, J.A. (2012). Turing Patterns in Deserts. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_67

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  • DOI: https://doi.org/10.1007/978-3-642-30870-3_67

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30869-7

  • Online ISBN: 978-3-642-30870-3

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