Stability analysis of coupled map lattices at locally unstable fixed points

Details Stability analysis of coupled map lattices at locally unstable fixed points Stability analysis of coupled map lattices at locally unstable fixed points

2004-07-07

arxiv.org/abs/nlin/0407014v2

European Physical Journal B 44 (2005) 229-239

Nonlinear Sciences

Chaotic Dynamics

22 pages, 6 figures, accepted for publication in European Physical Journal B

Scientific paper

10.1140/epjb/e2005-00119-2

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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