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Modal and wave synchronization in coupled self-excited oscillators.

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This study reveals that coupled bistable van der Pol oscillators exhibit ubiquitous modal synchronization. This non-conventional behavior, characterized by stable beating waves, appears in various system configurations and sizes.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Oscillator networks

Background:

  • Bistable van der Pol (BVdP) oscillators are fundamental in nonlinear dynamics.
  • Coupled oscillator systems often display synchronization and localization behaviors.
  • Modal synchronization, a non-conventional synchronization pattern, has been observed in specific BVdP systems.

Purpose of the Study:

  • To demonstrate the generic and ubiquitous nature of modal synchronization in linearly coupled identical BVdP oscillators.
  • To explore the parametric regimes where this unusual synchronization behavior emerges.
  • To investigate the influence of system size and internal resonances on synchronization patterns.

Main Methods:

  • Analysis of a system of linearly coupled identical BVdP oscillators.
  • Investigation across various parametric regimes, including weak coupling and small self-excitation.
  • Direct numerical simulations and analytical modeling of oscillator chains.

Main Results:

  • Stable beating attractors with synchronized mode amplitudes are observed.
  • Modal synchronization is found to be generic and ubiquitous under appropriate conditions.
  • Specific synchronization patterns, including two-wave and multi-wave synchronization, are identified for different numbers of coupled oscillators (N=2,3,5,6,7).
  • The N=4 case exhibits instability in two-wave synchronization due to internal resonances, leading to complex multi-wave patterns.

Conclusions:

  • Modal synchronization in coupled BVdP oscillators is a widespread phenomenon.
  • System parameters and internal resonances significantly influence the observed synchronization dynamics.
  • Analytical models successfully capture the dynamics of emergent beating waves.