STABILITY OF A STATIONARY CRITICAL STATE IN A MODEL OF CLUSTER FORMATION


Cite this article as:

Shapoval А. B. STABILITY OF A STATIONARY CRITICAL STATE IN A MODEL OF CLUSTER FORMATION. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 3, pp. 45-55. DOI: https://doi.org/10.18500/0869-6632-2011-19-3-45-55


The paper considers a self­organized critical process of clasterization. The stability of the equilibrium for infinite system of the differential equations approximating this process is proved.

DOI: 
10.18500/0869-6632-2011-19-3-45-55
Literature

1. Колмогоров А.Н. Локальная структура турбулентности в несжимаемой жидкости при очень больших числах Рейнольдса // ДАН СССР. 1941. Т. 30. С. 299.

2. Фриш У. Турбулентность. Наследие А.Н. Колмогорова. М.: ФАЗИС, 1998. 360 с.

3. March T.K., Chapman S.C., Dendy R.O., Merrifield J.A. Off-axis electron cyclotron heating and the sandpile paradigm for transport in tokamak plasmas // Phys. of Plasmas. 2004. Vol. 11. P. 659.

4. Писаренко В.Ф., Родкин М.В. Распределения с тяжелыми хвостами: Приложения к анализу катастроф. М.: ГЕОС, 2007. 240 с.

5. Bershadskii A. and Sreenivasan K.R. Multiscale self-organized criticality and powerful x-ray flares // Eur. Phys. J. B. 2003. Vol. 35. P. 513.

6. Amaral L.A.N., Cizeau P., Gopikrishnan P., Liu Y., Meyer M., Peng C.-K., Stanley H.E. Econophysics: Can statistical physics contribute to the science of economics? // Computer Physics Communications. 1999. Vol. 121–122. P. 145.

7. Шупер В.А. Самоорганизация городского расселения. М.: Наука, 1995. 166 с.

8. Bak P., Tang C., and Wiesenfeld K. Self-organized criticality: An explanation of 1/f noise // Phys. Rev. Lett. 1987. Vol. 59. P. 381.

9. Dhar D. Theoretical studies of self-organized criticality // Physica A. 2006. Vol. 369. P. 29.

10. Hemmer P.C. and Hansen A. The distribution of simultaneous fiber failures in fiber bundles // ASME J. Appl. Mech. 1992. Vol. 59. P. 909.

11. Hallgass R., Loreto V., Mazzella O., Paladin G., and Pietronero L. Earthquakes statistics and fractal faults // Phys. Rev. E. 1997. Vol. 56. P. 1346.

12. Carlson J.M., Langer J.S. Properties of earthquakes generated by fault dynamics // Phys. Rev. Lett. 1989. Vol. 62. P. 2632.

13. Blanter E.M., Shnirman M.G., Le Mouel J.-L., and Allegre C.J.  ̈ Scaling laws in blocks dynamics and dynamic self-organized criticality // Physics of the Earth and Planetary Interiors. 1997. Vol. 99. P. 295.

14. Dhar D., Majumdar S.N. Abelian sandpile model on the Bethe lattice // J. Physica A. 1990. Vol. 23. P. 4333.

15. Gabrielov A., Newman W.I., Turcotte D.L. An exactly soluble hierarchical clustering model: Inverse cascades, self-similarity, and scaling // Phys. Rev. E. 1999. Vol. 60. P. 5293.

16. Strahler A.N. Quantitative analysis of watershed morphology // Trans. Am. Geophys. Union. 1957. Vol. 38. P. 913.

17. Малинецкий Г.Г. Сценарии, стратегические риски, информационные технологии // Информационные технологии и вычислительные системы. 2002. No 4. С. 83.

18. Малинецкий Г.Г., Подлазов А.В., Кузнецов И.В. Мониторинг, анализ и прогноз опасностей как задачи национальной информационной системы // Информационные технологии и вычислительные системы. 2004. No 4 С. 119.

19. Bak P. How nature works: The science of self-organized criticality. New York: Springer-Verlag, Inc. 1996. 205 pp.

20. Bak P. and Paczuski M. Complexity, contingency, and criticality // Proceedings of the National Academy of Sciences of the USA. 1995. Vol. 92. P. 6689.

21. Blanter E.M., Shnirman M.G., Le Mouel J.-L. Temporal variation of predictability in a hierarchical model of dynamical self-organized criticality // Physics of the Earth and Planetary Interiors. 1999.Vol. 111. P. 317.

22. Shnirman M.G., Shapoval A.B. Variable predictability in deterministic dissipative sandpile // Nonlinear Processes in Geophysics. 2010. Vol. 17. P. 85.

23. Keilis-Borok V.I. Fundamentals of earthquake prediction: Four paradigms / in V.I. Keilis-Borok and A.A. Soloviev (eds.) Nonlinear dynamics of the lithosphere and earthquake prediction. Springer-Verlag, Heidelberg, 2003. P. 1.

24. Кузнецов И.В., Родкин М.В., Серебряков Д.В., Урядов О.Б. Иерархический подход к динамике преступности / В сб. Новое в синергетике. Новая реальность, новые проблемы, новое поколение. Часть 1. Под ред. Г.Г. Малинецкого. М.: Радиотехника, 2006. P. 103.

 

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@article{Шаповал -IzvVUZ_AND-19-3-45,
author = {А. B. Shapoval},
title = {STABILITY OF A STATIONARY CRITICAL STATE IN A MODEL OF CLUSTER FORMATION},
year = {2011},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {19},number = {3},
url = {https://old-andjournal.sgu.ru/en/articles/stability-of-stationary-critical-state-in-model-of-cluster-formation},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2011-19-3-45-55},pages = {45--55},issn = {0869-6632},
keywords = {Self­organized criticality,clustering,equilibrium,stability.},
abstract = {The paper considers a self­organized critical process of clasterization. The stability of the equilibrium for infinite system of the differential equations approximating this process is proved. }}