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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Log-periodicity can appear in a non-Markovian random walk even if there is perfect memory of its history

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Author(s):
de Lacerda, K. J. C. C. [1] ; Cressoni, J. C. [2] ; Viswanathan, G. M. [3, 4] ; da Silva, M. A. A. [2]
Total Authors: 4
Affiliation:
[1] Univ Sao Paulo, Dept Fis, FFCLRP, BR-14040901 Ribeirao Preto, SP - Brazil
[2] Univ Sao Paulo, Dept Ciencias Biomol, FCFRP, BR-14040903 Ribeirao Preto, SP - Brazil
[3] Univ Fed Rio Grande do Norte, Natl Inst Sci & Technol Complex Syst, BR-59078900 Natal, RN - Brazil
[4] Univ Fed Rio Grande do Norte, Dept Phys, BR-59078900 Natal, RN - Brazil
Total Affiliations: 4
Document type: Journal article
Source: EPL; v. 130, n. 2 APR 2020.
Web of Science Citations: 0
Abstract

The exactly solvable Elephant Random Walk (ERW) model introduced by Schutz and Trimper 15 years ago stimulated research that led to many new insights and advances in understanding anomalous diffusion. Such models have two distinct ingredients: i) long-range -possibly complete- memory of the past behavior and ii) a decision-making rule that makes use of the memory. These models are memory-neutral: the decision-making rule does not distinguish between short-term (or recent) memories and long-term (or old) memories. Here we relax the condition of memory neutrality, so that memory and decision-making become interconnected. We investigate the diffusive properties of random walks that evolve according to memory-biased decision processes and find remarkably rich phase diagrams, including a phase of log-periodic superdiffusion that may be associated with old memory and negative feedback regulating mechanisms. Our results overturn the conventional wisdom concerning the origin of log-periodicity in non-Markovian models. All previously known non-Markovian random walk models that exhibit log-periodicities in their behavior have incomplete (or damaged) memory of their history. Here we show that log-periodicity can appear even if the memory is complete, so long as there is a memory bias. (AU)

FAPESP's process: 11/06757-0 - Diffusive processes: random walkers with memory
Grantee:Marco Antonio Alves da Silva
Support Opportunities: Regular Research Grants
FAPESP's process: 11/13685-6 - Analytical and computational modelling of diffusive systems
Grantee:Marco Antonio Alves da Silva
Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil