Physica D 168–169 (2002) 142–151
New intermittencies in the chaotic synchronization
of two coupled 1D arrays of phase oscillators
L. Carlos L. Pando
Instituto de Fisica, Universidad Autónoma de Puebla, Apdo. Postal J-48, Puebla, Pue 72570, Mexico
Abstract
A model consisting of two identical unidirectionally coupled 1D arrays of phase oscillators is studied. The master array
is in the spatio-temporal chaos regime and is periodically driven. The time series of the distance between the arrays is the
main object of our study. As the unidirectional coupling between the arrays increases, a transition from a Markovian regime
to a noise regime in the time series is observed. Typically, this time series has a PDF whose core depends strongly on the
stroboscopic section and typically displays tails with power-law dependence. The kind of intermittency of this time series is
not characteristic of on–off intermittency, which typically arises in models of chaotic synchronization.
© 2002 Published by Elsevier Science B.V.
PACS: 05.45.+b; 02.30.Ks; 87.10.+e
Keywords: Intermittency; Phase oscillators; Chaotic synchronization
1. Introduction
During the last decade it has been shown that on–off intermittency is a typical behavior in nonlinear dynamical
systems [1]. It is observed when chaotic motion on an invariant manifold loses its stability when a control parameter
is changed [1]. It has been reported that on–off intermittency has also been observed in systems with large degrees of
freedom [2]. In on–off intermittency, the system spends long periods of time in the vicinity of the invariant manifold.
These intervals are interrupted by short bursts where the system moves away from the invariant manifold [1].
The problem of chaotic synchronization between two identical subsystems is a canonical example where on–off
intermittency can take place [3]. Here, the invariant manifold is the state where the variables of the subsystems
have the same values all the time. Chaotic synchronization is a vast field of research [4]. The important concept of
complete synchronization [3] refers to a state where the trajectories of two identical chaotic systems approach each
other exponentially fast. We explore this concept in the study of our models. There are other more subtle types of
synchronization which have been extensively considered [5].
The problem of synchronization between single arrays has been receiving special attention in the last few years.
For instance, chaotic synchronization between two 1D lattices of oscillators has been considered in [6]. As for
continuous in space systems, the onset of synchronization has been studied in several one-dimensional models [7],
such as pairs of coupled 1D Ginzburg–Landau equations and pairs of Kuramoto–Sivashinsky equations [7].
0167-2789/02/$ – see front matter © 2002 Published by Elsevier Science B.V.
PII:S0167-2789(02)00502-X