A FEW BASIC STRUCTURES DETERMINE THE BEHAVIOR OF A COUPLED MAP LATTICE

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.