SPATIALLY PERIODIC-ORBITS IN COUPLED-MAP LATTICES

We obtain the conditions that ensure the stability of spatially and te mporally periodic orbits of coupled-map lattices. The stability matric es can be put in a circulant and block circulant form. This allows us to reduce the problem to smaller matrices corresponding to the buildin g blocks of spatial periodicity. We find that additional conditions ar e imposed as we expand the size of the lattice. For the traveling-wave solution the analysis is considerably simplified. We have analyzed bo th the one-dimensional and higher-dimensional lattices.