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Intermittency transition to generalized synchronization in coupled time-delay systems.

D V Senthilkumar1, M Lakshmanan

  • 1Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli 620 024, India. skumar@cnld.bdu.ac.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
PubMed
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We reveal how two coupled time-delay systems achieve generalized synchronization (GS) through on-off intermittency. Different coupling methods lead to distinct synchronization behaviors and transition ranges.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Generalized synchronization (GS) is a complex phenomenon in coupled dynamical systems.
  • Understanding transition routes to GS is crucial for analyzing system behavior.
  • Time-delay systems introduce unique dynamics due to their history-dependent nature.

Purpose of the Study:

  • To investigate the transition mechanism to generalized synchronization in coupled piecewise linear time-delay systems.
  • To analyze the influence of different coupling configurations on the synchronization transition.
  • To explore the robustness of these transitions with respect to system parameters and time delays.

Main Methods:

  • Utilized the auxiliary system approach to study the transition to GS.

Related Experiment Videos

  • Employed analytical methods, including stability conditions for synchronized states.
  • Conducted numerical simulations to assess synchronization probability and sub-Lyapunov exponents.

    • Main Results:

    • The transition to GS occurs via an on-off intermittency route.
    • Error feedback coupling exhibits a broad range for intermittency transition, while direct feedback coupling shows a narrow range.
    • Intermittent dynamics manifest as periodic bursts (error feedback) or random bursts (direct feedback).

    Conclusions:

    • The distinct transition behaviors are attributed to differences in coupling configurations.
    • The findings are supported by analytical stability conditions and numerical evidence.
    • The study provides insights into intermittency synchronization in coupled time-delay systems.