For citation:
Malinetskii G. G., Podlazov A. V. Paradigm of self-organized criticality. Hierarchy of models and limits of predictability. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 5, pp. 89-106. DOI: 10.18500/0869-6632-1997-5-5-89-106
Paradigm of self-organized criticality. Hierarchy of models and limits of predictability
We considered the phenomenon of self-organized criticality (SOC). The SOC-systems are studied from the point of view of the branching processes theory. Transition from the critical behavior to non-critical one is demonstrated. The strict definition of criticality is given on the base of the «scale» value — a new statistical characteristic proposed. The hierarchy of SOC-models from the simplest branching processes to complex distributed system is built. The particular attention in the paper is paid to the problem of predictability in critical systems.
- Bak Р, Tang C, Wiesenfeld K. Self-organized criticality. Phys. Rev. A. 1988;38(1):364-374. DOI: 10.1103/PhysRevA.38.364.
- Sornette A, Sornette D. Self-Organized Criticality and Earthquakes. Europhys. Lett. 1989;9(3):197-202. DOI: 10.1209/0295-5075/9/3/002.
- Bak Р, Flyvbjerg H. Self-organization of cellular magnetic-domain patterns. Phys. Rev. А. 1992;45(4):2192-2200. DOI: 10.1103/PhysRevA.45.2192.
- Pietronero L, Tartaglia Р, Zhang Y—C. Theoretical studies of self-organized criticality. Physica А. 1991;173(1-2):22-44. DOI: 10.1016/0378-4371(91)90248-B.
- Dhar Р., Ramaswamy R. Exactly solved model of self-organized critical phenomena. Phys. Rev. Lett. 1989;63(16):1659-1662. DOI: 10.1103/PhysRevLett.63.1659.
- Ма Shang-Keng. Modern Theory Of Critical Phenomena. N.Y.: W. A. Benjamin; 1976. 561 p.
- Harris ТE. The Theory of Branching Processes. Berlin: Springer; 1963. 232 p.
- Podlazov AV. New aspects of self-organized criticality. Preprint Keldysh Institute of Applied Mathematics, No 86. M.; 1995. 10 p.
- Feller W. An Introduction to Probability Theory and Its Applications. N.Y.: Wiley; 1957. 669 p.
- Pepke SL, Carlson JM. Predictability of self-organizing systems. Phys. Rev. Е. 1994;50(1):236-242. DOI: 10.1103/PhysRevE.50.236.
- Janosi IM, Czirok А. Fractal clasters and self-organized criticality. Fractals. 1994;2(1):153-168. DOI: 10.1142/S0218348X94000156.
- Malinetskii GG, Mitin NA. Self-organized criticality. Rus. J. Phys. Chem. A. 1995;69(8):1513-1518.
- 190 reads