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Global phase synchronization in an array of time-delay systems.

R Suresh1, D V Senthilkumar, M Lakshmanan

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

We identified global phase synchronization (GPS) in coupled chaotic systems. Synchronization occurs sequentially, with asynchronous systems forming clusters before joining the main group.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Mackey-Glass time-delay systems exhibit complex, non-phase-coherent chaotic attractors.
  • Understanding synchronization in coupled chaotic systems is crucial for various scientific fields.

Purpose of the Study:

  • To identify and characterize global phase synchronization (GPS) in a linear array of coupled Mackey-Glass time-delay systems.
  • To investigate the mechanism of synchronization, specifically sequential synchronization and cluster formation.

Main Methods:

  • Utilized nonlinear transformations to derive phase-coherent attractors from non-phase-coherent ones.
  • Estimated instantaneous phases, phase differences, average phases, and frequencies.
  • Employed recurrence analysis and the concept of localized sets for validation.

Main Results:

  • Demonstrated the emergence of global phase synchronization (GPS) in the array.
  • Showed that GPS is achieved through sequential synchronization dependent on coupling strength.
  • Observed asynchronous systems forming intermediate clusters before synchronizing with the main cluster.

Conclusions:

  • Global phase synchronization is achievable in arrays of coupled chaotic time-delay systems.
  • Sequential synchronization and intermediate cluster formation are key mechanisms for achieving GPS.
  • The findings are robust and validated by multiple analytical approaches.