Narrow log-periodic modulations in non-Markovian random walks.
Phys Rev E
; 96(6-1): 062143, 2017 Dec.
Article
em En
| MEDLINE
| ID: mdl-29347279
ABSTRACT
What are the necessary ingredients for log-periodicity to appear in the dynamics of a random walk model? Can they be subtle enough to be overlooked? Previous studies suggest that long-range damaged memory and negative feedback together are necessary conditions for the emergence of log-periodic oscillations. The role of negative feedback would then be crucial, forcing the system to change direction. In this paper we show that small-amplitude log-periodic oscillations can emerge when the system is driven by positive feedback. Due to their very small amplitude, these oscillations can easily be mistaken for numerical finite-size effects. The models we use consist of discrete-time random walks with strong memory correlations where the decision process is taken from memory profiles based either on a binomial distribution or on a delta distribution. Anomalous superdiffusive behavior and log-periodic modulations are shown to arise in the large time limit for convenient choices of the models parameters.
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MEDLINE
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En
Ano de publicação:
2017
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Article