Self-organized criticality

Self-organized criticality is when certain complex systems naturally reach a state where even a small change can cause events of any size, from tiny effects to massive ones.[1] The system does not need careful tuning or outside control to get to this point; it gets there on its own through its normal processes.[2] The idea was first described in 1987 by physicist Per Bak and his colleagues Chao Tang and Kurt Wiesenfeld. They used a simple sandpile model to show that adding grains of sand could cause anything from small slides to large avalanches, without changing the basic rules.[1] This concept is important because it helps explain why many natural and human-made systems have sudden, unpredictable events that follow patterns found in nature, such as power laws.[3]

A main feature of self-organized criticality is that the events it produces are scale-invariant. This means small and large events follow the same statistical rules.[4] For example, both tiny tremors and huge earthquakes follow the same pattern, as described by the Gutenberg–Richter law.[5][6] The same applies to forest fires, where a spark might burn one tree or thousands of hectares,[7] and to financial markets, where small price changes and major crashes have similar patterns.[8] Other examples include solar flares from the Sun,[9] which can be weak or massive but follow the same rules, and bursts of brain activity called neuronal avalanches, which vary in size but follow similar mathematical patterns.[10]

Self-organized criticality is different from normal critical points in physics, which usually need precise adjustments, like setting the exact temperature or pressure.[11] In self-organized systems, the critical state happens automatically through the system’s regular behavior.[2] This is an example of an emergent property, large-scale patterns appear from the interactions of many small parts following simple rules.[3] In the sandpile model, as grains are added, the pile gets steeper until a single grain triggers an avalanche. The size of the avalanche cannot be predicted from the trigger itself; only the overall pattern of many avalanches over time can be understood.[1]

Studying self-organized criticality helps scientists understand systems that are unpredictable in detail but predictable in overall patterns.[6] It has been used to model things like stock market ups and downs,[8] internet traffic jams,[12] species extinctions,[13] and highway congestion.[14] The main challenge is that while the general statistics of these systems can be studied, it is almost impossible to know exactly when a big event will happen.[3] This makes self-organized criticality both a useful tool for explaining patterns and a limitation for predicting exact events. Research in this field uses physics, mathematics, computer models, and real-world data to explore how complexity and unpredictability naturally emerge in many systems.[2][4]

  • Critical brain hypothesis
  • Critical exponents
  • Detrended fluctuation analysis
  • Dual-phase evolution
  • Self-organization
  • Scale invariance
  • Self-organized criticality control

References

  1. ↑ 1.0 1.1 1.2 Bak, Per; Tang, Chao; Wiesenfeld, Kurt (1987-07-27). "Self-organized criticality: An explanation of the 1/f noise". Physical Review Letters. 59 (4): 381–384. doi:10.1103/PhysRevLett.59.381.
  2. ↑ 2.0 2.1 2.2 Bak, Per (1999). How nature works: the science of self-organized criticality (1., softcover pr ed.). New York [Heidelberg]: Copernicus. ISBN 978-0-387-98738-5.
  3. ↑ 3.0 3.1 3.2 Jensen, Henrik Jeldtoft (2000). Self-organized criticality: emergent complex behavior in physical and biological systems. Cambridge lecture notes in physics ([Repr.], transferred to digital print ed.). Cambridge: Cambridge Univ. Press. ISBN 978-0-521-48371-1.
  4. ↑ 4.0 4.1 Christensen, Kim; Moloney, Nicholas R. (2005). Complexity and criticality. Imperial College Press advanced physics texts. London: Imperial College Press. ISBN 978-1-86094-504-5.
  5. ↑ Gutenberg, B.; Richter, C. F. (1955-10-22). "Magnitude and Energy of Earthquakes". Nature. 176 (4486): 795–795. doi:10.1038/176795a0. ISSN 0028-0836.
  6. ↑ 6.0 6.1 Turcotte, Donald L (1999-09-28). "Self-organized criticality". Reports on Progress in Physics. 62 (10): 1377–1429. doi:10.1088/0034-4885/62/10/201. ISSN 0034-4885.
  7. ↑ Malamud, Bruce D.; Morein, Gleb; Turcotte, Donald L. (1998-09-18). "Forest Fires: An Example of Self-Organized Critical Behavior". Science. 281 (5384): 1840–1842. doi:10.1126/science.281.5384.1840.
  8. ↑ 8.0 8.1 Sornette, Didier, ed. (2006). Critical phenomena in natural sciences: chaos, fractals, selforganization and disorder: concepts and tools. Springer series in synergetics (2nd ed.). Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg. ISBN 978-3-540-30882-9.
  9. ↑ Charbonneau, Paul; McIntosh, Scott W.; Liu, Han-Li; Bogdan, Thomas J. (2001-11-01). "Avalanche models for solar flares (Invited Review)". Solar Physics. 203 (2): 321–353. doi:10.1023/A:1013301521745. ISSN 1573-093X.
  10. ↑ Beggs, John M.; Plenz, Dietmar (2003-12-03). "Neuronal Avalanches in Neocortical Circuits". Journal of Neuroscience. 23 (35): 11167–11177. doi:10.1523/JNEUROSCI.23-35-11167.2003. ISSN 0270-6474. PMID 14657176.
  11. ↑ Stanley, H. Eugene (1987). Introduction to phase transitions and critical phenomena. New York: Oxford University Press. ISBN 978-0-19-505316-6.
  12. ↑ Valverde, Sergi; Solé, Ricard V (2002-09-15). "Self-organized critical traffic in parallel computer networks". Physica A: Statistical Mechanics and its Applications. 312 (3): 636–648. doi:10.1016/S0378-4371(02)00872-5. ISSN 0378-4371.
  13. ↑ Solé, Ricard V.; Manrubia, Susanna C. (1996-07-01). "Extinction and self-organized criticality in a model of large-scale evolution". Physical Review E. 54 (1): R42 – R45. doi:10.1103/PhysRevE.54.R42.
  14. ↑ Nagel, Kai; Paczuski, Maya (1995-04-01). "Emergent traffic jams". Physical Review E. 51 (4): 2909–2918. doi:10.1103/PhysRevE.51.2909.


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