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Phase synchronization in time-delay systems.

D V Senthilkumar1, M Lakshmanan, J Kurths

  • 1Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli, 620 024, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
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This study identifies phase synchronization in coupled chaotic time-delay systems with hyperchaotic attractors. Researchers observed transitions from no synchronization to phase and generalized synchronization with increasing coupling strength.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

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

Purpose of the Study:

  • To identify and characterize phase synchronization in coupled chaotic time-delay systems exhibiting hyperchaotic attractors.
  • To investigate the transitions between different synchronization behaviors as a function of coupling strength.

Main Methods:

  • Coupled piecewise linear and Mackey-Glass time-delay systems were used.
  • Recurrence quantification analysis was employed to characterize transitions.
  • Phase differences were analyzed using attractor transformations.

Related Experiment Videos

  • Lyapunov exponents were monitored to identify synchronization changes.

    • Main Results:

    • Phase synchronization was successfully identified in coupled time-delay systems with hyperchaotic attractors.
    • A clear transition from nonsynchronized behavior to phase synchronization, and then to generalized synchronization, was observed with increasing coupling strength.
    • These transitions were consistently characterized by recurrence quantification analysis, phase difference analysis, and Lyapunov exponent changes.

    Conclusions:

    • Phase synchronization is achievable in chaotic time-delay systems with hyperchaotic attractors.
    • The study demonstrates a predictable sequence of synchronization transitions (none -> phase -> generalized) based on coupling strength.
    • The findings provide new insights into synchronization phenomena in complex dynamical systems with time delays.