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Published on: June 8, 2022
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Synchronization behavior in a ternary phase model
N DeTal1, H Taheri2, K Wiesenfeld1
1Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
Chaos (Woodbury, N.Y.)
|July 4, 2019
Summary
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.
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.
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