Year: 2008
Type: article
Abstract: We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of four phases, for this system: (i) classical nonpersistence, (ii) classical persistence, (iii) log-periodic nonpersistence, and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however, log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.
Source: Physical Review E
Authors: Marco Antonio Alves da Silva, G. M. Viswanathan, A. S. Ferreira, J. C. Cressoni
Institutions: Universidade de São Paulo, Universidade Federal de Alagoas
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2039338939