Self-organized criticality

Self-organized criticality (SOC) is one of a number of physical mechanisms believed to underly the widespread observation in nature of certain complex structures and patterns, such as fractals, power laws and 1/f noise. Technically speaking, it refers to dynamical systems which have a critical point as an attractor, resulting in the natural evolution of spatial and temporal scale invariance without the need to tune control parameters to precise values. First identified by Per Bak, Chao Tang and Kurt Wiesenfeld (BTW) in a seminal paper published in 1987 in Physical Review Letters, the phenomenon sparked great scientific interest and its concepts have been enthusiastically applied across a wide compass of fields and topics, ranging from earthquakes and solar flares to biological evolution, neuroscience and the economy.

SOC is typically observed in slowly-driven non-equilibrium systems with extended degrees of freedom and a high level of nonlinearity. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that guarantee a system will display SOC.

Theoretical models

 * Bak-Tang-Wiesenfeld sandpile model
 * Forest fire models
 * Olami-Feder-Christensen model
 * Bak-Sneppen model