Analysis of spatiotemporally periodic behavior in lattices of coupled piecewise monotonic maps - art. no. 017202

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 s patial and temporal periodicities and their stability can be studied throug h 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 a pplies for arbitrary temporal periods and is valid for all coupled map latt ice systems coupled in a translationally invariant manner with stability ma trices which are irreducible and non-negative, as in the present case. Our analysis could be useful in the analysis of stability regions and bifurcati on behavior in a variety of spatially extended systems.