TY  - JOUR
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
T1  - Comment on "Phase synchronization in discrete chaotic systems"
N2  - Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
T1  - Comment on "Intermittency in chaotic rotations"
Y1  - 2001
ER  - 
TY  - BOOK
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
T1  - Synchronization : a universal concept in nonlinear sciences
T3  - Cambridge nonlinear science series
Y1  - 2001
SN  - 0-521-59285-2
VL  - 12
PB  - Cambridge Univ. Press
CY  - Cambridge
ET  - 1st paperback ed., repr
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
T1  - Comment on "Intermittency in chaotic rotations"
N2  - Lai et al. [Phys. Rev. E 62, R29 (2000)] claim that the angular velocity of the phase point moving along the chaotic trajectory in a properly chosen projection (the instantaneous frequency) is intermittent. Using the same examples, namely the Rössler and the Lorenz systems, we show the absence of intermittency in the dynamics of the instantaneous frequency.This is confirmed by demonstrating that the phase dynamics exhibits normal diffusion. We argue that the nonintermittent behavior is generic.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
T1  - Detecting direction of coupling in interacting oscillators
N2  - We propose a method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. The technique is applicable to both noisy and chaotic systems that can be nonidentical or even structurally different. We introduce an index that quantifies the asymmetry in coupling.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Ivanov, Plamen Ch.
A1  - Nuenes Amaral, Luís A.
A1  - Goldberger, Ary L.
A1  - Havlin, Shlomo
A1  - Rosenblum, Michael
A1  - Stanley, H. Eugene
A1  - Struzik, Zbigniew R.
T1  - From 1/f noise to multifractal cascades in heartbeat dynamics
Y1  - 2001
SN  - 1054-1500
ER  -