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.