Phase Order in Chaotic Maps and in Coupled Map Lattices

By defining a direction phase as the direction of two sequential iterations of the logistic map, a transition of a net direction phase M from zero to a finite value as the parameter μ increases is found. Near the transition point μ₀ a scaling M~(μ-μ₀)^α with α0ex0ex=0ex0ex0.5 is obtained. The order state of the direction phases in a coupled map lattice is also studied. A phase synchronization of the direction phases is found although the lattices still remain chaotic.