Self-organized critical system with no stationary attractor state.

A simple model economy with interacting producers and consumers is introduced. When driven by extreme dynamics, the model self-organizes not to an attractor state, but to an asymptote, on which the economy has a constant rate of deflation, is critical, and exhibits avalanches of activity with power-law distributed sizes. This example demonstrates that self-organized critical behavior occurs in a larger class of systems than so far considered: systems not driven to an attractive fixed point, but, e.g., an asymptote, may also display self-organized criticality.