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::Self-organized criticality

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In physics, self-organized criticality (SOC) is a property of (classes of) dynamical systems that 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 concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper<ref name=Bak1987> {{#invoke:Citation/CS1|citation |CitationClass=journal }} Papercore summary: http://papercore.org/Bak1987.</ref> published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity <ref name=Bak1995> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref> arises in nature. Its concepts have been enthusiastically applied across fields as diverse as geophysics, physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology <ref name=TurcotteSmalleySolla85> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref name=SmalleyTurcotteSolla85> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref name=LinkenkaerHansen2001> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref name=Beggs2003> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref name=Chialvo2004> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref name=Boettcher1999> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref name=Fraiman2009> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref name=deArcangelis2006> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref name=Poil2012> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref><ref name=Kitzbichler> {{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref> <ref name=Chialvo2010>{{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref> <ref name=Tagliazucchi2012>{{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref> <ref name=Haimovici2013>{{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref> 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.


Self-organized criticality sections
Intro   Overview    Examples of self-organized critical dynamics    See also   References   Further reading   

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