Analysis of spatiotemporally periodic behavior in lattices of coupled piecewise monotonic maps

We study the stability of spatiotemporally periodic orbits in 1-d lattices of piecewise monotonic maps coupled via translationally invariant coupling and periodic boundary conditions. States of such systems have independent spatial and temporal periodicities and their stability can be studied through the analysis of a single, uniquely identified reduced matrix of size k X k when the system size is M x M, for M = kN, a multiple of k. This result applies for arbitrary temporal periods and is valid for all coupled map lattice systems coupled in a translationally invariant manner with stability matrices which are irreducible and non-negative, as in the present case. Our analysis could be useful in the analysis of stability regions and bifurcation behavior in a variety of spatially extended systems.