We consider the stability properties of spatial and temporal periodic orbits of one-dimensional coupled-map lattices. The stability matrices for them are of the block-circulant form. This helps us to reduce the problem of stability of spatially periodic orbits to the smaller orbits corresponding to the building blocks of spatial periodicity, enabling us to obtain the conditions for stability in terms of those for smaller orbits.
R. E. Amritkar, Gade, P. M., Gangal, A. D., and Dr. V . M. Nandakumaran, “Stability of periodic orbits of coupled-map lattices”, Physical Review A, vol. 44, pp. R3407–R3410, 1991.