Self-organized criticality

Self-organized criticality (SOC) is one of a number of physical mechanisms believed to underly the widespread occurrence of certain complex structures and patterns observed in nature, such as fractals, power laws and 1/f noise. Technically speaking, it refers to (classes of) dynamical systems which have a critical point as an attractor. Their macroscopic behaviour thus displays the spatial and/or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to precise values.

The phenomenon was first identified by Per Bak, Chao Tang and Kurt Wiesenfeld (BTW) in a seminal paper published in 1987 in Physical Review Letters. These and related concepts have been enthusiastically applied across a diverse range of fields and topics, notably including earthquakes and other geophysical problems, biological evolution, solar flares 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.

Examples of self-organized critical dynamics

Theoretical models

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

See also

• 1/f noise
• Complex systems
• Fractals
• Power laws
• Scale invariance
• Self-organization

References

• Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality. New York: Copernicus. ISBN 0-387-94791-4. 

• Bak, P. and Paczuski, M. (1995). "Complexity, contingency, and criticality". Proceedings of the National Academy of Sciences of the USA 92: 6689–6696.

• Bak, P. and Sneppen, K. (1993). "Punctuated equilibrium and criticality in a simple model of evolution". Physical Review Letters 71: 4083–4086. DOI:10.1103/PhysRevLett.71.4083. Research Blogging.

• Bak, P., Tang, C. and Wiesenfeld, K. (1987). "Self-organized criticality: an explanation of $1/f$ noise". Physical Review Letters 59: 381–384. DOI:10.1103/PhysRevLett.59.381. Research Blogging.

• Bak, P., Tang, C. and Wiesenfeld, K. (1988). "Self-organized criticality". Physical Review A 38: 364–374. DOI:10.1103/PhysRevA.38.364. Research Blogging.

• Buchanan, M. (2000). Ubiquity. London: Weidenfeld & Nicolson. ISBN 0-7538-1297-5. 

• Jensen, H. J. (1998). Self-Organized Criticality. Cambridge: Cambridge University Press. ISBN 0-521-48371-9. 

• Paczuski, M. (2005). "Networks as renormalized models for emergent behavior in physical systems". arXiv.org: physics/0502028.

• Turcotte, D. L. (1997). Fractals and Chaos in Geology and Geophysics. Cambridge: Cambridge University Press. ISBN 0-521-56733-5. 

• Turcotte, D. L. (1999). "Self-organized criticality". Reports on Progress in Physics 62: 1377–1429. DOI:10.1088/0034-4885/62/10/201. Research Blogging.