Simplest Possible Self-Organized Critical System
- 5 February 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 76 (6) , 940-943
- https://doi.org/10.1103/physrevlett.76.940
Abstract
In order to pinpoint the nature of self-organized criticality, a simplest possible system exhibiting the phenomenon is introduced and analyzed. Its phase space is fully parametrized by two integer variables, one describing the state of a medium (sandpile), the other describing the state of a disturbance (avalanche) propagating in the medium, modifying it in the process. For asymptotically large systems, a scaling limit is obtained in which the system's state and dynamics is given by two real numbers and a simple partial differential equation. These results provide a full and transparent description of the dynamics that drives this system critical and keeps it in that state.Keywords
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