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Phase-induced stability in a parametric dimer.

M Copelli1, K Lindenberg

  • 1Department of Chemistry and Biochemistry 0340, University of California San Diego, La Jolla, California 92093-0340, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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This study on coupled oscillators shows that antiphase modulations reduce parametric resonance. The two-oscillator model effectively mirrors the behavior of larger, infinite systems.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Oscillatory Systems

Background:

  • Coupled oscillators are fundamental in various scientific fields.
  • Parametric modulations can induce resonance and instability.
  • Understanding phase differences is crucial for system behavior.

Purpose of the Study:

  • To investigate the influence of phase difference on parametric resonance in coupled oscillators.
  • To analyze the synchronization properties of the system.
  • To compare the two-oscillator model with mean-field models.

Main Methods:

  • Analytical solutions for a model of two coupled oscillators.
  • Periodic parametric modulations with a phase difference theta.
  • Investigation of resonance regions and synchronization phenomena.

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Main Results:

  • The model exhibits a rich dependence of parametric resonance regions on the phase difference theta.
  • Antiphase modulations (theta = pi) reduce parametric resonance for significant coupling and damping.
  • The two-oscillator model captures qualitative behaviors of infinite systems.

Conclusions:

  • The phase difference critically affects parametric resonance in coupled oscillators.
  • The two-oscillator model serves as a valuable and analytically tractable approximation for collective phenomena.
  • Results provide insights into synchronization and collective parametric instability.