The main trend of some blow-up systems is disturbed by log-periodic oscillations infinitely accelerating when approaching the blow-up time. Explanation of such behavior typical e.g. for seismic and economic phenomena could give an insight into the nature of blow-up time rising in this case as the condensation of constant phase points of oscillations. Log-periodic oscillations are observed in the classical democratic fiber bundle model whit the strength of bundles generated by means of random number generator of scanty depth. In this case possible strength values belong to a periodic set. And the model transforms this periodic input to log-periodic output. Periodic events are quite worldwide, so one can assume that log-periodicity in other systems originate from the same transformation.

Mathematical modelling in actual problems of science and technics