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 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.

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 and its concepts have been enthusiastically applied across a diverse range of fields and topics, ranging from earthquakes and other geophysical problems to 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.