Eur. Phys. J. B 44, 229-239 (2005)
https://doi.org/10.1140/epjb/e2005-00119-2

Stability analysis of coupled map lattices at locally unstable fixed points

¹ Center for Interdisciplinary Plasma Science, Max-Planck-Institut für extraterrestrische Physik, 85740 Garching, Germany
² Department of Theory and Data Analysis, Institute for Frontier Areas of Psychology and Mental Health, Wilhelmstr. 3a, 79098 Freiburg, Germany
³ Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany

Corresponding author: ^a haa@igpp.de

Received: 18 October 2004
Published online: 20 April 2005

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.