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Comment on "Phase synchronization in discrete chaotic systems".

M G Rosenblum1, A S Pikovsky, J Kurths

  • 1Department of Physics, Potsdam University, Am Neuen Palais 10, PF 601553, D-14415 Potsdam, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
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This study challenges Chen et al.

Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Complex systems

Background:

  • Coupled chaotic systems exhibit phase synchronization.
  • Chen et al. proposed a phase definition for discrete chaotic systems.
  • This definition was applied to coupled map lattices.

Purpose of the Study:

  • To critically evaluate Chen et al.'s phase definition for discrete systems.
  • To investigate the applicability of phase synchronization to discrete maps.
  • To demonstrate limitations of the proposed phase concept.

Main Methods:

  • Analysis of discrete chaotic systems.
  • Development of counterexamples to test the phase definition.
  • Comparison with phase synchronization in continuous systems.

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Main Results:

  • The angle variable proposed by Chen et al. does not meet the criteria for a proper phase.
  • Two counterexamples illustrate the failure of the extended phase definition.
  • The generalizability of phase synchronization to discrete maps is questioned.

Conclusions:

  • Chen et al.'s phase definition for discrete systems is inadequate.
  • The concept of phase synchronization may not extend reliably to discrete chaotic maps.
  • Further research is needed to define phase and synchronization in discrete systems.