V. Franceschini et C. Vernia, A FEW BASIC STRUCTURES DETERMINE THE BEHAVIOR OF A COUPLED MAP LATTICE, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 57(3), 1998, pp. 2757-2762
The stability and formation of structures in lattices of diffusively c
oupled logistic maps are investigated for high nonlinearity and medium
and large coupling. Two stability statements are given that relate th
e presence of the predominant attractors, i.e., cycles and quasiperiod
ic traveling waves, to the stability of a few simple periodic structur
es. They are supported by strong numerical evidence. Furthermore, they
are justified through the description of some mechanisms that connect
the formation of a stable structure to the cycles of the uncoupled la
ttice. As an important consequence, for given parameter values, an app
roximate prediction of the behavior of the lattice is allowed.