Narrow log-periodic modulations in non-Markovian random walks

Author(s)

Diniz, R. M. B. ; Cressoni, J. C. ; da Silva, M. A. A. ; Mariz, A. M. ; de Araujo, J. M.

• Document type: Journal article
• Source: PHYSICAL REVIEW E; v. 96, n. 6, p. 7-pg., 2017-12-26.

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 frommemory 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. (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
• FAPESP's process: 17/01176-6 - Memory effects and characterization in stochastic processes
• Grantee: Marco Antonio Alves da Silva
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil