Collective behavior of a coupled-map system with a conserved quantity

We present the results of a numerical investigation of, and supporting analytic arguments for, the behavior of coupled sine maps with a locally conserved variable on a square lattice, with and without noise. By varying parameters we find two distinct conservation-induced routes to chaos: One is a first-order transition from a periodic 2-cycle phase with broken time-translational invariance and long-range, striped, spatial order, to a chaotic, …