Nontrivial collective behavior in coupled maps on fractal lattices

The collective behavior of locally coupled-map lattices is investigated when the connections are defined on fractal geometries, such as generalized Sierpinski gaskets embedded in -dimensional Euclidean spaces. The collective states are described through the mean fields of the networks. Periodic global attractors are observed as functions of the parameters of the systems, with no indications of collective quasiperiodicities which are common in high-dimensional regular lattices. The influence of the connectivity on the emergence of nontrivial collective behavior in coupled chaotic systems is discussed.