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Synchronization behavior in a ternary phase model.

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Summary
This summary is machine-generated.

Localized traveling waves in nonlinear systems synchronize due to Fourier mode coupling. Adding disorder causes first-order transitions, unlike the Kuramoto model, revealing novel synchronization dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Wave phenomena

Background:

  • Traveling-wave solutions in nonlinear Schrödinger equations arise from Fourier mode synchronization.
  • Reduced models exhibit novel ternary coupling for mode interactions.

Purpose of the Study:

  • Analyze a phase model with ternary coupling under quenched disorder.
  • Investigate transitions to partial and complete synchronization.
  • Compare findings with the Kuramoto model.

Main Methods:

  • Analysis of a reduced phase model with quenched disorder (Gaussian and uniform).
  • Exploration of synchronization transitions.
  • Derivation and solution of an infinite-oscillator limit.
  • Comparison with Kuramoto model phenomenology.

Main Results:

  • First-order phase transitions with hysteresis observed for both Gaussian and uniform disorder.
  • Synchronization behavior differs significantly from the Kuramoto model.
  • Theoretical predictions for transitions derived from the infinite-oscillator limit.

Conclusions:

  • Quenched disorder induces novel first-order synchronization transitions in ternary coupled systems.
  • The model's nonlocal ternary coupling contributes to its unique dynamics.
  • Disordered nonlinear systems exhibit complex synchronization patterns beyond standard models.