  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.
