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Low-dimensional dynamics for higher-order harmonic, globally coupled phase-oscillator ensembles
Chen Chris Gong1, Arkady Pikovsky2
1Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 32, 14476 Potsdam, Germany.
Physical Review. E
|January 23, 2020
Summary
This study extends the Kuramoto model for higher-order harmonic coupling in oscillatory systems. The new low-dimensional theory explains complex phenomena like asymmetrical clustering in synchronized systems.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Theoretical Physics
Background:
- The Kuramoto model is a popular mean-field theory for synchronization in oscillatory systems.
- Existing theories are limited to first-order harmonic coupling and low dimensions in the thermodynamic limit for higher-order couplings.
Purpose of the Study:
- To extend the Watanabe and Strogatz formulation for a low-dimensional description of systems with higher-order harmonic coupling.
- To analyze systems of arbitrary size with all-to-all coupling via higher-order modes.
- To explain phenomena like asymmetrical clustering observed in higher-order coupled systems.
Main Methods:
- Extension of the Watanabe and Strogatz formulation for higher-order harmonic coupling.
- Application of the developed theory to a second harmonic globally coupled model.
- Analytical explanation of asymmetrical clustering and comparison with first-order coupling phenomena.
Main Results:
- A low-dimensional analytical theory for systems with arbitrary size and higher-order harmonic coupling was developed.
- The theory successfully explains the asymmetrical clustering observed in a second harmonic globally coupled model.
- New phenomena not seen in first-order coupling were identified and discussed.
Conclusions:
- The developed theory provides a powerful tool for understanding complex synchronization behaviors in higher-order coupled oscillatory systems.
- The findings offer insights into phenomena beyond the scope of the standard Kuramoto model.
- This work advances the theoretical framework for analyzing synchronization in diverse scientific fields.
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