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Transition from phase to generalized synchronization in time-delay systems.

D V Senthilkumar1, M Lakshmanan, J Kurths

  • 1Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli-620024, India. skumar@cnld.bdu.ac.in

Chaos (Woodbury, N.Y.)
|July 8, 2008
PubMed
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Researchers identified phase synchronization in time-delay systems, a feat previously unrealized. This breakthrough enables understanding complex system dynamics and transitions between synchronization states.

Area of Science:

  • Nonlinear Dynamics
  • Complex Systems
  • Time-Delay Systems

Background:

  • Phase synchronization is well-studied in chaotic systems without delay.
  • It has not been previously realized in time-delay systems with non-phase-coherent attractors.

Purpose of the Study:

  • To identify and characterize phase synchronization in coupled nonidentical time-delay systems.
  • To investigate transitions between different synchronization regimes (none, phase, generalized).

Main Methods:

  • Introduced a novel transformation to capture the phase of non-phase-coherent attractors.
  • Analyzed instantaneous phase locking conditions (phase and mean frequency).
  • Utilized recurrence-based indices (generalized autocorrelation, probability of recurrence, Lyapunov exponents) for characterization.

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Main Results:

  • Successfully identified phase synchronization in coupled piecewise linear and Mackey-Glass time-delay systems.
  • Demonstrated a transition from no synchronization to phase synchronization, and then to generalized synchronization with increasing coupling strength.
  • Quantified synchronization regimes using recurrence-based indices and Lyapunov exponent transitions.

Conclusions:

  • Phase synchronization is achievable in time-delay systems even with highly non-phase-coherent attractors.
  • The developed phase transformation method is effective for analyzing such systems.
  • Recurrence-based indices and Lyapunov exponents provide robust characterization of synchronization transitions.