VESTNIK of Samara University. Aerospace and Mechanical EngineeringVESTNIK of Samara University. Aerospace and Mechanical Engineering2542-04532541-7533Samara National Research University198610.18287/2541-7533-2012-0-2(33)-266-273UnclassifiedLog-periodic oscillations in hierarchical modelsPivovarovaA. S.<p>Post-graduate Student of the Physics Department</p>a-pivovarova@mail.ruSamara State Aerospace University180620121122662730912201409122014Copyright © 2015, VESTNIK of the Samara State Aerospace University2015<p>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 tobuild the generalization of this model we introduce the dependence of an influence exponent on an ultrametricdistance between agents. Much attention is being paid to the problem of critical point universality which is investigatedby comparison of probability density functions of the crash times corresponding to systems with varioustotal numbers of agents.</p>Математическое моделированиелогопериодические колебания и степенной ростультраметрическое расстояниеиерархические структурыфинансовые крахиMathematical modelinglog periodic power lawultrametric distancehierarchical structurefinancial crashes