Symmetry breaking bifurcations in a circular chain of N coupled logistic maps

A circular chain of N cells with logistic dynamics, coupled together with symmetric nearest neighbor coupling and periodic boundary conditions is investigated. For certain coupling parameters we observe bifurcation of a stable state into two types of period two solutions. By using the symmetry of this Coupled Map Lattice model, we show that the bifurcated system only can have periodic solutions with symmetry group corresponding to certain subgroups of the full symmetry group of the system.