Strong Ordering by Non-uniformity of Thresholds in a Coupled Map Lattice

The coupled map lattice by Olami {\it et al.} [Phys. Rev. Lett. {\bf 68}, 1244 (1992)] is ``doped'' by letting just {\it one} site have a threshold, $T^{*}_{\rm max}$, bigger than the others. On an $L \times L$ lattice with periodic boundary conditions this leads to a transition from avalanche sizes of about one to exactly $L^2$, and after each avalanche stresses distributes among only five distinct values, $\tau_{k}$, related to the parameters $\alpha$ and $T^{*}_{\rm max}$ by $\tau_{k}= k\alpha T^{*}_{\rm max}$ where $k=0,1,2,3,4$. This result is independent of lattice size. The transient times are inversely proportional to the amount of doping and increase linearly with $L$.