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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Phase-flip transition in nonlinear oscillators coupled by dynamic environment.

Amit Sharma1, Manish Dev Shrimali, Syamal Kumar Dana

  • 1The LNM Institute of Information Technology, Jaipur 302031, India.

Chaos (Woodbury, N.Y.)
|July 5, 2012
PubMed
Summary

Indirectly coupled nonlinear oscillators synchronize and exhibit phase-flip transitions. This study analyzes these dynamics in periodic and chaotic regimes, confirmed experimentally.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Synchronization phenomena

Background:

  • Nonlinear oscillators are fundamental in various scientific fields.
  • Coupling mechanisms significantly influence oscillator dynamics.
  • Indirect coupling through a common medium presents unique synchronization behaviors.

Purpose of the Study:

  • To investigate synchronization and phase-flip transitions in indirectly coupled nonlinear oscillators.
  • To analyze the parameter space governing these transitions for different oscillator types.
  • To provide experimental validation for observed dynamical transitions.

Main Methods:

  • Analysis of coupled nonlinear systems (Landau-Stuart, Rössler, van der Pol oscillators).
  • Characterization of dynamical transitions using average phase difference, frequency, and Lyapunov exponents.
  • Experimental implementation using electronic oscillator circuits.

Main Results:

  • Indirect coupling induces synchronization in both periodic and chaotic regimes.
  • Phase-flip transitions between in-phase and anti-phase synchronization were observed and mapped.
  • Experimental results with van der Pol oscillators confirm the theoretical findings.

Conclusions:

  • Indirect coupling is a crucial factor in achieving synchronization and complex dynamical transitions.
  • The phase-flip transition is a robust phenomenon observable across different nonlinear oscillator models.
  • This research offers insights into controlling and predicting synchronization in coupled systems.