Bak, Per; Tang, Chao; Wiesenfeld, Kurt Self-organized criticality. (English) Zbl 1230.37103 Phys. Rev. A (3) 38, No. 1, 364-374 (1988). Summary: We show that certain extended dissipative dynamical systems naturally evolve into a critical state, with no characteristic time or length scales. The temporal ‘fingerprint’ of the self-organized critical state is the presence of flicker noise or \(1/f\) noise; its spatial signature is the emergence of scale-invariant (fractal) structure. Cited in 5 ReviewsCited in 323 Documents MSC: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 82C05 Classical dynamic and nonequilibrium statistical mechanics (general) 37A60 Dynamical aspects of statistical mechanics 37B15 Dynamical aspects of cellular automata 37N25 Dynamical systems in biology 82D37 Statistical mechanics of semiconductors Keywords:self-organized criticality; critical point as attractor; fractal geometry; \(1/f\) noise; power laws × Cite Format Result Cite Review PDF Full Text: DOI References: [1] W. H. Press, Comm. Mod. Phys. C7 pp 103– (1978) [2] P. Dutta, Rev. Mod. Phys. 53 pp 497– (1981) · doi:10.1103/RevModPhys.53.497 [3] B. Mandelbrot, in: The Fractal Geometry of Nature (1982) · Zbl 0504.28001 [4] P. Bak, Phys. Rev. Lett. 59 pp 381– (1987) · doi:10.1103/PhysRevLett.59.381 [5] H. Haken, Rev. Mod. Phys. 47 pp 67– (1975) · doi:10.1103/RevModPhys.47.67 [6] P. L. Nolan, Astrophys. J. 246 pp 494– (1981) · doi:10.1086/158949 [7] A. Lawrence, Nature 325 pp 694– (1987) · doi:10.1038/325694a0 [8] I. McHardy, Nature 325 pp 696– (1987) · doi:10.1038/325696a0 [9] B. B. Mandelbrot, Water Resour. Res. 5 pp 321– (1969) · doi:10.1029/WR005i002p00321 [10] R. F. Voss, Phys. Rev. B 13 pp 556– (1976) · doi:10.1103/PhysRevB.13.556 [11] K. L. Schick, Nature 251 pp 599– (1974) · doi:10.1038/251599a0 [12] B. B. Mandelbrot, SIAM (Soc. Ind. Appl. Math.) Rev. 10 pp 422– (1968) [13] L. P. Kadanoff, Phys. Today 39 (1986) [14] , in: Phase Transitions and Critical Phenomena (1972) [15] A. van der Ziel, Physica 16 pp 359– (1950) · doi:10.1016/0031-8914(50)90078-4 [16] C. Tang, Phys. Rev. Lett. 58 pp 1161– (1987) · doi:10.1103/PhysRevLett.58.1161 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.