Long range action in networks of chaotic elements

Details Long range action in networks of chaotic elements Long range action in networks of chaotic elements

2005-05-27

arxiv.org/abs/math/0505610v1

Mathematics

Dynamical Systems

15 pages

Scientific paper

10.1088/0951-7715/19/2/005

We show that under certain simple assumptions on the topology (structure) of networks of strongly interacting chaotic elements a phenomenon of long range action takes place, namely that the asymptotic (as time goes to infinity) dynamics of an arbitrary large network is completely determined by its boundary conditions. This phenomenon takes place under very mild and robust assumptions on local dynamics with short range interactions. However, we show that it is unstable with respect to arbitrarily weak local random perturbations.

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