Mapping Self-Organized Criticality onto Criticality

Details Mapping Self-Organized Criticality onto Criticality Mapping Self-Organized Criticality onto Criticality

1994-11-28

arxiv.org/abs/adap-org/9411002v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

17 pages total

Scientific paper

10.1051/jp1:1995129

We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical point. More precisely, SOC is shown to result from the tuning of the {\em order parameter} to a vanishingly small, but {\em positive} value, thus ensuring that the corresponding control parameter lies exactly at its critical value for the underlying transition. This clarifies the role and nature of the {\em very slow driving rate} common to all systems exhibiting SOC. This mechanism is shown to apply to models of sandpiles, earthquakes, depinning, fractal growth and forest-fires, which have been proposed as examples of SOC.

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