Pm. Gade et Re. Amritkar, SPATIALLY PERIODIC-ORBITS IN COUPLED-MAP LATTICES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47(1), 1993, pp. 143-154
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.