Formation, Stability and Predictability of Structures in Coupled Map Lattices

Some significant non-chaotic behaviors of the lattices ofcoupled logistic maps are analyzed. In particular, the review concerns the organization of cycles for small coupling andthe fundamental role played by heteroclinic cycles and quasiperiodic traveling waves. Moreover, we point to the existence of a few elementary cycles the stability of which determines that of almost all non-chaotic structures of any size, in particular for high nonlinearity and medium and large coupling.This allows an approximate prediction of which attractors can occur for given parameter values.