Strong Ordering by Non-uniformity of Thresholds in a Coupled Map Lattice
Abstract
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
∗
max
, bigger than the others. On an
L×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,
τ
k
, related to the parameters
α
and
T
∗
max
by
τ
k
=kα
T
∗
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
.