Volume 83, Number 2, July 2008
Article Number 20001
Number of page(s) 6
Section General
Published online 01 July 2008
EPL, 83 (2008) 20001
DOI: 10.1209/0295-5075/83/20001

Intricate dynamics of a deterministic walk confined in a strip

D. Boyer

Instituto de Física, Universidad Nacional Autónoma de México - Apartado Postal 20-364, 01000 México D.F., México

received 1 May 2008; accepted in final form 2 June 2008; published July 2008
published online 1 July 2008

We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at some intermediate values of the domain width, when, while drifting, the walk performs long intermittent backward excursions. As the width is increased, evidence of a transition from ballistic motion to a weakly non-ergodic regime is shown, characterized by sudden inversions of the drift velocity with a probability slowly decaying with time, as 1/t at leading order. Excursion durations, first-passage times and the dynamics of unvisited targets follow power law distributions. For parameter values below this scaling regime, precursory patterns in the form of "wild" outliers are observed, in close relation with the presence of log-oscillations in the probability distributions. We discuss the connections between this model and several evolving biological systems.

02.50.-r - Probability theory, stochastic processes, and statistics.
05.40.Fb - Random walks and Lévy flights.
89.75.-k - Complex systems.

© EPLA 2008