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, $T_{\max }^{\ast }$, 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 $T_{\max }^{\ast }$ by ${\tau }_k=k\alpha T_{\max }^{\ast }$ 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 $L$.

12 pages uuencoded postscript, including figures. Accepted for publication in Physica Scripta.

References in corpus (2)

• Self-Organized Criticality in Non-conserved Systems
• Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators

Cited by in corpus (5)

• Statistical Physics of Fracture, Friction and Earthquake
• Random Neighbor Theory of the Olami-Feder-Christensen Earthquake Model
• Self - organized - criticality and synchronization in pulse coupled relaxation oscillator systems: the Olami, Feder and Christensen model and the Feder and Feder model
• Simulation study of the inhomogeneous Olami-Feder-Christensen model of earthquakes
• Spatial heterogeneity in earthquake fault-like systems