Self-organized criticality

Self-organized criticality (SOC) is a property of

Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.[1]

Models of self-organized criticality

In chronological order of development:

• Stick-slip model of fault failure^[11][3]
• Bak–Tang–Wiesenfeld sandpile
• Forest-fire model
• Olami–Feder–Christensen model
• Bak–Sneppen model

Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the critical exponents^[12][13]), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average ^{[clarification needed]}.

It has been argued that the BTW "sandpile" model should actually generate 1/f² noise rather than 1/f noise.^[14] This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models generally produce 1/f^a spectra, with a<2.^[15] Other simulation models were proposed later that could produce true 1/f noise.^[16]

In addition to the nonconservative theoretical model mentioned above ^{[clarification needed]}, other theoretical models for SOC have been based upon information theory,^[17]

Key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.

Self-organized criticality in nature

SOC has become established as a strong candidate for explaining a number of natural phenomena, including:

• The magnitude of earthquakes (Gutenberg–Richter law) and frequency of aftershocks (Omori law) ^[11][3]
• Fluctuations in economic systems such as
  financial markets (references to SOC are common in econophysics) ^[22][23]
• The evolution of proteins[24]^[25]
• Forest fires ^{[clarification needed][26]}
• Neuronal avalanches in the cortex^{[8][27][28][29]}
• Acoustic emission from fracturing materials^[30]

Despite the numerous applications of SOC to understanding natural phenomena, the universality of SOC theory has been questioned. For example, experiments with real piles of rice revealed their dynamics to be far more sensitive to parameters than originally predicted.^[31][1] Furthermore, it has been argued that 1/f scaling in EEG recordings are inconsistent with critical states,^[32] and whether SOC is a fundamental property of neural systems remains an open and controversial topic.^[33]

Self-organized criticality and optimization

It has been found that the avalanches from an SOC process make effective patterns in a random search for optimal solutions on graphs.^[34] An example of such an optimization problem is

• 1/f noise
• Complex systems
• Critical brain hypothesis
• Critical exponents
• Detrended fluctuation analysis, a method to detect power-law scaling in time series.
• Dual-phase evolution, another process that contributes to self-organization in complex systems.
• Fractals
• Ilya Prigogine, a systems scientist who helped formalize dissipative system behavior in general terms.
• Power laws
• Red Queen hypothesis
• Scale invariance
• Self-organization
• Self-organized criticality control

References