Stability analysis of coupled map lattices
at locally unstable fixed points |
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Authors: | Email author" target="_blank">H?AtmanspacherEmail author T?Filk H?Scheingraber |
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Institution: | (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 |
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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. |
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Keywords: | |
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