BLOWUP WITH COMPLEX EXPONENTS. LOGPERIODIC OSCILLATIONS IN THE DEMOCRATIC FIBER BUNDLE MODEL
Cite this article as:
Podlazov А. V. BLOWUP WITH COMPLEX EXPONENTS. LOGPERIODIC OSCILLATIONS IN THE DEMOCRATIC FIBER BUNDLE MODEL. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 2, pp. 15-30. DOI: https://doi.org/10.18500/0869-6632-2011-19-2-15-30
The main trend of some blowup systems is disturbed by logperiodic oscillations infinitely accelerating when approaching the blowup point. Explanation of such behavior typical e.g. for seismic and economic phenomena could give an insight into the nature of blowup point rising in this case as the condensation of constant phase points of oscillations. This viewpoint is a particular case of the more general approach that treats not oscillations as a disturbance of the growing trend, but the trend itself as a result of oscillatory process. Logperiodic oscillations indicate about the discrete scale invariance of described phenomenon. One can easily establish the connection of theirs with other its examples, such as considered here selfsimilar fractals or diffusion in anisotropic quenched random media. However these examples presuppose the presence of discrete levels of organization in the system nontrivial of themselves. We show that logperiodic oscillations arise in the classical democratic fiber bundle model with the strength of bundles generated by means of random number generator of limited depth. In this case possible strength values belong to a periodic set. And the nonlinear model just transforms this periodic input to the logperiodic output. Periodic events are quite worldwide, so one can assume that logperiodicity in other systems originates from a similar transformation.
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BibTeX
author = {А. V Podlazov},
title = {BLOWUP WITH COMPLEX EXPONENTS. LOGPERIODIC OSCILLATIONS IN THE DEMOCRATIC FIBER BUNDLE MODEL},
year = {2011},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {19},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/blowup-with-complex-exponents-logperiodic-oscillations-in-the-democratic-fiber-bundle-0},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2011-19-2-15-30},pages = {15--30},issn = {0869-6632},
keywords = {Logperiodic oscillations,blowup growth,critical phenomena,discreet scale invariance,democratic fiber bundle model,computer simulation.},
abstract = {The main trend of some blowup systems is disturbed by logperiodic oscillations infinitely accelerating when approaching the blowup point. Explanation of such behavior typical e.g. for seismic and economic phenomena could give an insight into the nature of blowup point rising in this case as the condensation of constant phase points of oscillations. This viewpoint is a particular case of the more general approach that treats not oscillations as a disturbance of the growing trend, but the trend itself as a result of oscillatory process. Logperiodic oscillations indicate about the discrete scale invariance of described phenomenon. One can easily establish the connection of theirs with other its examples, such as considered here selfsimilar fractals or diffusion in anisotropic quenched random media. However these examples presuppose the presence of discrete levels of organization in the system nontrivial of themselves. We show that logperiodic oscillations arise in the classical democratic fiber bundle model with the strength of bundles generated by means of random number generator of limited depth. In this case possible strength values belong to a periodic set. And the nonlinear model just transforms this periodic input to the logperiodic output. Periodic events are quite worldwide, so one can assume that logperiodicity in other systems originates from a similar transformation. }}