The stability and formation of structures in lattices of diffusively coupled logistic maps are investigated for high nonlinearity and medium and large coupling. Two stability statements are given that relate the presence of the predominant attractors, i.e., cycles and quasiperiodic traveling waves, to the stability of a few simple periodic structures. 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 lattice. As an important consequence, for given parameter values, an approximate prediction of the behavior of the lattice is allowed.
A few basic structures determine the behavior of a coupled map lattice / Franceschini, Valter; Vernia, Cecilia. - In: PHYSICAL REVIEW E. - ISSN 1063-651X. - STAMPA. - 57:(1998), pp. 2757-2762.