Periodicity manifestations in the turbulent regime of the globally coupled map lattice

We revisit the globally coupled map lattice. We show that in the so called turbulent regime various periodic cluster attractor states are formed, even though the coupling between the maps are very small relative to the nonlinearity in the element maps. Most outstanding is a maximally symmetric three cluster attractor in period-3 motion, due to the foliation of the period-3 window of the element logistic maps. An analytical approach is proposed which successfully explains the systematics of various periodicity manifestations in the turbulent regime. The linear stability of the period-3 cluster attractors is investigated.