Log-periodic oscillations in hierarchical models


We explore the log-periodic behavior which is known to precede the critical events of some complex systems. Particularly, we consider the hierarchical model of financial crashes introduced by A. Johansen and D. Sornette which reproduces the log-periodic power law behavior of the price before the critical point. In order to build the generalization of this model we introduce the dependence of an influence exponent on an ultrametric distance between agents. Much attention is being paid to the problem of critical point universality which is investigated by comparison of probability density functions of the crash times corresponding to systems with various total numbers of agents.

About the authors

A. S. Pivovarova

Samara State Aerospace University

Author for correspondence.
Email: a-pivovarova@mail.ru

Russian Federation

Post-graduate Student of the Physics Department


  1. Sornette, D. A hierarchical model of financial crashes [Text] / D. Sornette, A. Johansen // Physica A - 1998 - Vol. 261. - P. 581 - 598.
  2. Sornette, D. Stock market crashes, Precursors and Replicas [Text] / D. Sornette, A. Johansen, J.-Ph. Bouchaud // Journal de Physique, France. - 1996 - Vol. 6. - P. 167 - 175.
  3. Бикулов, А. Х. Иерархическая динамическая модель финансового рынка вблизи точки обвала и p-адический математический анализ [Текст] / А. Х. Бикулов, А. П. Зубарев, Л. В. Кайдалова // Вестн. Самар. гос. техн. ун-та. Сер. Физ.-мат. науки. - 2006 - № 42. - С. 135 - 140.
  4. Подлазов, А. В. Режимы с обострением с комплексными показателями. Лог-периодические колебания в модели разрыва пучка волокон [Текст] / А. В. Подлазов // Препринты ИПМ им. М.В. Келдыша. - 2009 - № 35. - 22 с.
  5. Huang, Y. Spontaneous generation of discrete scale invariance in growth models [Text] / Y. Huang, G. Ouillon, H. Saleur, D. Sornette // Phys. Rev. E - 1997 - Vol. 55. - P. 6433 - 6447.
  6. Tostesen, E. Dynamics of hierarchically clustured cooperative agents [Text] / E. Tostesen - Cand. Scient. Thesis, University of Copenhagen, 1995.
  7. Cont, R. Herd behavior and aggregate fluctuations in speculative markets [Text] / R. Cont, J.P. Bouchaud // Macroeconomic dynamics - 2000 - Vol. 4, No.2.



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