Fluctuations at the self-organized critical state

Avalanche dynamics is defined as coupled internal motion at two separate time scales. The state parameter S(t) measures the amount of tension or potential energy stored in the system. Fluctuations of S(t) = F-d(up arrow) - F-a(down arrow) are caused by the action F-d on S of the driving force, giving rise to slow, continuous motion, and the antagonistic action F-a of a relaxation force causing rapid, discrete events (avalanches). The arrows indicate the directions of the forces (increase or decrease). A state parameter may be chosen such that both forces act as repellers in state space. Self-organized criticality (SOC) emerges when F-a is an internal force that exists if, and only if, F-d is present. When this contingency condition is fulfilled, the two antagonistic forces trap the system trajectory inside a SOC attractor, which is a state-space region of overlapping basins for the two types of motion. The conclusions are based primarily on the case of river meandering dynamics, described in the paper.