Comment on "Phase synchronization in discrete chaotic systems".
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.
Rosenblum
M G
MG
Department of Physics, Potsdam University, Am Neuen Palais 10, PF 601553, D-14415 Potsdam, Germany.
Pikovsky
A S
AS
Kurths
J
J