Self-organized criticality

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
An image of the 2d Bak-Tang-Wiesenfeld sandpile, the original model of self-organized criticality.

Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.

The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper[1] published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity[2] arises in nature. Its concepts have been applied across fields as diverse as geophysics,[3] physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology[4][5][6][7] and others.

SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. 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.

Overview[edit]

Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.

The term self-organized criticality was first introduced in Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous—and therefore plausible as a source of natural complexity—rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. An alternative view is that SOC appears when the criticality is linked to a value of zero of the control parameters.[8]

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[edit]

In chronological order of development:

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[10][11]), 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 this model[clarification needed] would actually generate 1/f2 noise rather than 1/f noise.[12] This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models generally produce 1/fa spectra, with a<2.[13] Other simulation models were proposed later that could produce true 1/f noise,[14].

In addition to the nonconservative theoretical model mentioned above[clarification needed], other theoretical models for SOC have been based upon information theory,[15] mean field theory,[16] the convergence of random variables,[17] and cluster formation.[18] A continuous model of self-organised criticality is proposed by using tropical geometry.[19]

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[edit]

The relevance of SOC to the dynamics of real sand has been questioned.

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

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.[24][1] Furthermore, it has been argued that 1/f scaling in EEG recordings are inconsistent with critical states,[25] and whether SOC is a fundamental property of neural systems remains an open and controversial topic.[26]

Self-organized criticality and optimization[edit]

It has been found that the avalanches from an SOC process make effective patterns in a random search for optimal solutions on graphs.[27] An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.

See also[edit]

References[edit]

  1. ^ a b c Bak, P.; Tang, C.; Wiesenfeld, K. (1987). "Self-organized criticality: an explanation of 1/f noise". Physical Review Letters. 59 (4): 381–384. Bibcode:1987PhRvL..59..381B. doi:10.1103/PhysRevLett.59.381. PMID 10035754. Papercore summary: http://papercore.org/Bak1987.
  2. ^ Bak, P.; Paczuski, M. (1995). "Complexity, contingency, and criticality". Proceedings of the National Academy of Sciences. 92 (15): 6689–6696. Bibcode:1995PNAS...92.6689B. doi:10.1073/pnas.92.15.6689. PMC 41396. PMID 11607561.
  3. ^ a b c Smalley, R. F. Jr; Turcotte, D. L.; Solla, S. A. (1985). "A renormalization group approach to the stick-slip behavior of faults". Journal of Geophysical Research. 90 (B2): 1894. Bibcode:1985JGR....90.1894S. doi:10.1029/JB090iB02p01894. S2CID 28835238.
  4. ^ Dmitriev, Andrey; Dmitriev, Victor (2021-01-20). "Identification of Self-Organized Critical State on Twitter Based on the Retweets' Time Series Analysis". Complexity. 2021: e6612785. doi:10.1155/2021/6612785. ISSN 1076-2787.
  5. ^ K. Linkenkaer-Hansen; V. V. Nikouline; J. M. Palva & R. J. Ilmoniemi. (2001). "Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations". The Journal of Neuroscience. 21 (4): 1370–1377. doi:10.1523/JNEUROSCI.21-04-01370.2001. PMC 6762238. PMID 11160408.
  6. ^ a b J. M. Beggs & D. Plenz (2006). "Neuronal Avalanches in Neocortical Circuits". The Journal of Neuroscience. 23 (35): 11167–77. doi:10.1523/JNEUROSCI.23-35-11167.2003. PMC 6741045. PMID 14657176.
  7. ^ Chialvo, D. R. (2004). "Critical brain networks". Physica A. 340 (4): 756–765. arXiv:cond-mat/0402538. Bibcode:2004PhyA..340..756R. doi:10.1016/j.physa.2004.05.064. S2CID 15922916.
  8. ^ Gabrielli, A; Caldarelli, G; Pietronero, L (2000). "Invasion Percolation with Temperature and the Nature of SOC in Real Systems". Physical Review E. 62 (6 Pt A): 7638–7641. arXiv:cond-mat/9910425. doi:10.1103/PhysRevE.62.7638. PMID 11138032. S2CID 20510811.
  9. ^ a b Turcotte, D. L.; Smalley, R. F. Jr; Solla, S. A. (1985). "Collapse of loaded fractal trees". Nature. 313 (6004): 671–672. Bibcode:1985Natur.313..671T. doi:10.1038/313671a0. S2CID 4317400.
  10. ^ Tang, C.; Bak, P. (1988). "Critical exponents and scaling relations for self-organized critical phenomena". Physical Review Letters. 60 (23): 2347–2350. Bibcode:1988PhRvL..60.2347T. doi:10.1103/PhysRevLett.60.2347. PMID 10038328.
  11. ^ Tang, C.; Bak, P. (1988). "Mean field theory of self-organized critical phenomena". Journal of Statistical Physics (Submitted manuscript). 51 (5–6): 797–802. Bibcode:1988JSP....51..797T. doi:10.1007/BF01014884. S2CID 67842194.
  12. ^ Jensen, H. J.; Christensen, K.; Fogedby, H. C. (1989). "1/f noise, distribution of lifetimes, and a pile of sand". Physical Review B. 40 (10): 7425–7427. Bibcode:1989PhRvB..40.7425J. doi:10.1103/physrevb.40.7425. PMID 9991162.
  13. ^ Laurson, Lasse; Alava, Mikko J.; Zapperi, Stefano (15 September 2005). "Letter: Power spectra of self-organized critical sand piles". Journal of Statistical Mechanics: Theory and Experiment. 0511. L001.
  14. ^ Maslov, S.; Tang, C.; Zhang, Y. - C. (1999). "1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes". Phys. Rev. Lett. 83 (12): 2449–2452. arXiv:cond-mat/9902074. Bibcode:1999PhRvL..83.2449M. doi:10.1103/physrevlett.83.2449. S2CID 119392131.
  15. ^ Dewar, R. (2003). "Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states". Journal of Physics A: Mathematical and General. 36 (3): 631–641. arXiv:cond-mat/0005382. Bibcode:2003JPhA...36..631D. doi:10.1088/0305-4470/36/3/303. S2CID 44217479.
  16. ^ Vespignani, A.; Zapperi, S. (1998). "How self-organized criticality works: a unified mean-field picture". Physical Review E. 57 (6): 6345–6362. arXiv:cond-mat/9709192. Bibcode:1998PhRvE..57.6345V. doi:10.1103/physreve.57.6345. hdl:2047/d20002173. S2CID 29500701.
  17. ^ Kendal, WS (2015). "Self-organized criticality attributed to a central limit-like convergence effect". Physica A. 421: 141–150. Bibcode:2015PhyA..421..141K. doi:10.1016/j.physa.2014.11.035.
  18. ^ Hoffmann, H. (2018). "Impact of Network Topology on Self-Organized Criticality". Physical Review E. 97 (2): 022313. Bibcode:2018PhRvE..97b2313H. doi:10.1103/PhysRevE.97.022313. PMID 29548239.
  19. ^ Kalinin, N.; Guzmán-Sáenz, A.; Prieto, Y.; Shkolnikov, M.; Kalinina, V.; Lupercio, E. (2018-08-15). "Self-organized criticality and pattern emergence through the lens of tropical geometry". Proceedings of the National Academy of Sciences. 115 (35): E8135–E8142. arXiv:1806.09153. doi:10.1073/pnas.1805847115. ISSN 0027-8424. PMC 6126730. PMID 30111541.
  20. ^ Phillips, J. C. (2014). "Fractals and self-organized criticality in proteins". Physica A. 415: 440–448. Bibcode:2014PhyA..415..440P. doi:10.1016/j.physa.2014.08.034.
  21. ^ Phillips, J. C. (2021). "Synchronized attachment and the Darwinian evolution of Coronaviruses CoV-1 and CoV-2". Physica A. 581: 126202. arXiv:2008.12168. Bibcode:2021PhyA..58126202P. doi:10.1016/j.physa.2021.126202. PMC 8216869. PMID 34177077.
  22. ^ Poil, SS; Hardstone, R; Mansvelder, HD; Linkenkaer-Hansen, K (Jul 2012). "Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks". Journal of Neuroscience. 32 (29): 9817–23. doi:10.1523/JNEUROSCI.5990-11.2012. PMC 3553543. PMID 22815496.
  23. ^ Caldarelli, G; Di Tolla, F; Petri, A (1996). "Self Organization and Annealed Disorder in Fracturing Processes" (PDF). Physical Review Letters. 77 (12): 2503–08. Bibcode:1996PhRvL..77.2503C. doi:10.1103/PhysRevLett.77.2503. PMID 10061970. S2CID 5462487.
  24. ^ Frette, V.; Christinasen, K.; Malthe-Sørenssen, A.; Feder, J; Jøssang, T; Meaken, P (1996). "Avalanche dynamics in a pile of rice". Nature. 379 (6560): 49–52. Bibcode:1996Natur.379...49F. doi:10.1038/379049a0. S2CID 4344739.
  25. ^ Bédard, C.; Kröger, H.; Destexhe, A. (2006). "Does the 1/f frequency scaling of brain signals reflect self-organized critical states?". Physical Review Letters. 97 (11): 118102. arXiv:q-bio/0608026. doi:10.1103/PhysRevLett.97.118102. PMID 17025932. S2CID 1036124.
  26. ^ Hesse, J.; Gross, T. (2014). "Self-organized criticality as a fundamental property of neural systems". Front Syst Neurosci. 8: 166. doi:10.3389/fnsys.2014.00166. PMC 4171833. PMID 25294989.
  27. ^ Hoffmann, H.; Payton, D. W. (2018). "Optimization by Self-Organized Criticality". Scientific Reports. 8 (1): 2358. Bibcode:2018NatSR...8.2358H. doi:10.1038/s41598-018-20275-7. PMC 5799203. PMID 29402956.

Further reading[edit]