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Transition to intermittent chaotic synchronization.

Liang Zhao1, Ying-Cheng Lai, Chih-Wen Shih

  • 1Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary
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Coupled chaotic oscillators show intermittent synchronization. The transition differs for phase-coherent (Rössler) and phase-incoherent (Lorenz) systems, explained by Lyapunov exponents and periodic orbits.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Coupled chaotic oscillators can display intermittent synchronization, a phenomenon where dynamics align temporarily.
  • This synchronization occurs in random intervals within the weakly coupling regime.

Purpose of the Study:

  • To investigate how the geometric properties of chaotic attractors influence the transition to intermittent synchronization.
  • To differentiate the synchronization transition mechanisms for phase-coherent and phase-incoherent chaotic systems.

Main Methods:

  • Analysis of coupled chaotic systems, specifically Rössler (phase-coherent) and Lorenz (phase-incoherent) systems.
  • Examination of the role of coupling strength in triggering synchronization.
  • Theoretical framework development using Lyapunov exponents and unstable periodic orbits.

Related Experiment Videos

Main Results:

  • Phase-coherent attractors (Rössler) exhibit immediate intermittent synchronization upon introducing coupling.
  • Phase-incoherent attractors (Lorenz) require stronger coupling for the onset of intermittent synchronization.
  • Distinct transition behaviors are observed based on attractor geometry.

Conclusions:

  • The geometric nature of chaotic attractors fundamentally impacts the transition to intermittent synchronization.
  • Lyapunov exponents and unstable periodic orbits provide a theoretical basis for understanding these distinct synchronization dynamics.