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Stability analysis of coupled map lattices at locally unstable fixed points

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  • H. Atmanspacher
  • T. Filk
  • H. Scheingraber

Abstract

Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for exploring fundamental features of CMLs, such as their stability properties. Since CMLs can be considered as graphs, we apply methods of spectral graph theory to analyze their stability at locally unstable fixed points for different updating rules, different coupling scenarios, and different types of neighborhoods. Numerical studies are found to be in excellent agreement with our theoretical results. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Suggested Citation

  • H. Atmanspacher & T. Filk & H. Scheingraber, 2005. "Stability analysis of coupled map lattices at locally unstable fixed points," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 44(2), pages 229-239, March.
    • Handle: RePEc:spr:eurphb:v:44:y:2005:i:2:p:229-239
    DOI: 10.1140/epjb/e2005-00119-2
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    1. Christos Pitelis & Roger Sugden & James R. Wilson, 2006. "Introduction," Chapters, in: Christos Pitelis & Roger Sugden & James R. Wilson (ed.), Clusters and Globalisation, chapter 1, Edward Elgar Publishing.
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    Cited by:

    1. Dobyns, York & Atmanspacher, Harald, 2006. "Information flow between weakly interacting lattices of coupled maps," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 755-767.

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