Self-organized criticality. (English) Zbl 1230.37103

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.


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
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[1] W. H. Press, Comm. Mod. Phys. C7 pp 103– (1978)
[2] P. Dutta, Rev. Mod. Phys. 53 pp 497– (1981)
[3] B. Mandelbrot, in: The Fractal Geometry of Nature (1982) · Zbl 0504.28001
[4] P. Bak, Phys. Rev. Lett. 59 pp 381– (1987)
[5] H. Haken, Rev. Mod. Phys. 47 pp 67– (1975)
[6] P. L. Nolan, Astrophys. J. 246 pp 494– (1981)
[7] A. Lawrence, Nature 325 pp 694– (1987)
[8] I. McHardy, Nature 325 pp 696– (1987)
[9] B. B. Mandelbrot, Water Resour. Res. 5 pp 321– (1969)
[10] R. F. Voss, Phys. Rev. B 13 pp 556– (1976)
[11] K. L. Schick, Nature 251 pp 599– (1974)
[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)
[16] C. Tang, Phys. Rev. Lett. 58 pp 1161– (1987)
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