Symbolic dynamics of coupled map lattices.
We present a method to reduce the [FORMULA: SEE TEXT] dynamics of coupled map lattices (CMLs) of N invertibly coupled unimodal maps to a sequence of N-bit symbols. We claim that the symbolic description is complete and provides for the identification of all fixed points, periodic orbits, and dense orbits as well as an efficient representation for studying pattern formation in CMLs. We give our results for CMLs in terms of symbolic dynamical concepts well known for one-dimensional chaotic maps, including generating partitions, Gray orderings, and kneading sequences. An example utilizing coupled quadratic maps is given.
U.S. Army Aviation and Missile Command, AMSRD-AMR-WS-ST, Redstone Arsenal, Alabama 35898, USA.
Shawn D
SD
Pethel
Ned J
NJ
Corron
Erik
E
Bollt