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Optimal global synchronization of partially forced Kuramoto oscillators
Joyce S Climaco1, Alberto Saa1
1Department of Applied Mathematics, University of Campinas, 13083-859 Campinas, São Paulo, Brazil.
Chaos (Woodbury, N.Y.)
|August 3, 2019
Summary
This study optimizes global synchronization in Kuramoto oscillator networks by strategically applying external forces. The best synchronization occurs when forced oscillators have natural frequencies furthest from the external driving frequency.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Global synchronization is crucial in many natural and engineered systems.
- Kuramoto oscillator networks are a standard model for studying synchronization phenomena.
- External periodic forces can influence network synchronization dynamics.
Purpose of the Study:
- To investigate global synchronization in random Kuramoto networks with partially forced oscillators.
- To develop an effective low-dimensional model for analyzing synchronization.
- To identify optimal strategies for achieving global synchronization through external forcing.
Main Methods:
- Dimensional reduction approach to create a two-dimensional model.
- Analytical derivation of critical parameters for synchronization onset.
- Numerical simulations to validate theoretical predictions.
- Development of an optimization scheme for forced oscillator selection.
Main Results:
- An effective two-dimensional model accurately describes the system.
- Analytical predictions for critical synchronization parameters were obtained.
- The optimal strategy involves forcing oscillators with natural frequencies maximally distant from the external driving frequency.
- Exhaustive numerical simulations corroborated these findings.
Conclusions:
- The study provides a method to optimize global synchronization in Kuramoto networks.
- The findings suggest that strategic application of external forces can enhance collective behavior.
- Results offer insights into natural systems where synchronization is important for function or evolution.
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