Self-organized criticality

In physics, self-organized criticality (SOC) is a property of (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, and is considered to be one of the mechanisms by which complexity arises in nature. Its concepts have been enthusiastically applied across fields as diverse as geophysics, cosmology, solar physics, biology and ecology, economics and sociology, quantum physics and others.

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.

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.