Self-organized criticality

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Self-organized criticality , also known as self-organized criticality ( SOC ), is a phenomenon that can occur in dynamic systems .

A dynamic system is in a critical state when the parameters of the system correspond to a phase transition . In a self-organized critical system, the parameters of the system approach with time by itself to the critical point (the critical point in this case is an attractor ). From this follows the special feature of such systems that they show the typical properties of a critical state largely independently of the choice of the initial parameters.

Typical properties of critical systems such as scale invariance and 1 / f noise can be observed in many areas. Examples are the strength of earthquakes ( Gutenberg-Richter law ), the size of avalanches or the frequency of words ( Zipf's law ). It seems unlikely that the parameters of such systems are at a critical point purely by chance. Here, self-organized criticality offers itself as an explanatory model for the frequent occurrence of critical properties, because no external control of the parameters is required. Complex structures arise spontaneously solely due to the interaction of individual elements of the system.

Although many models are already known that show self-organized criticality, no general condition is known so far from which self-organized criticality follows.

Examples

  • Bak -Tang-Wiesenfeld model for avalanches
  • Bak-Sneppen model for evolution
  • Drossel - Schwabl model for forest fires
  • Olami-Feder-Christensen model for earthquakes

swell

  1. ↑ Per Bak, Chao Tang and Kurt Wiesenfeld: Self-organized criticality: an explanation of 1 / ƒ noise . In: Physical Review Letters . tape 59 , no. 4 , 1987, pp. 381-384 , doi : 10.1103 / PhysRevLett.59.381 .
  2. ↑ Per Bak and Kim Sneppen: Punctuated equilibrium and criticality in a simple model of evolution . In: Physical Review Letters . tape  71 , no. 24 , 1993, pp. 4083-4086 , doi : 10.1103 / PhysRevLett.71.4083 .
  3. ↑ B. Drossel and F. Schwabl: Self-organized critical forest-fire model . In: Physical Review Letters . tape 69 , no. 11 , 1992, pp. 1629-1632 , doi : 10.1103 / PhysRevLett.69.1629 .
  4. ↑ Z. Olami, HJS Feder and K. Christensen: Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes . In: Physical Review Letters . tape 68 , no. 8 , 1992, pp. 1244-1247 , doi : 10.1103 / PhysRevLett.68.1244 .