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Directed acyclic decomposition of Kuramoto equations
1Department of Mathematics and Computer Science, Auburn University at Montgomery, Montgomery, Alabama 36116, USA and Department of Mathematics Michigan State University, East Lansing, Michigan 48824, USA.
Chaos (Woodbury, N.Y.)
|October 3, 2019
Summary
This study introduces a novel framework for analyzing synchronization in complex Kuramoto networks. The method decomposes large networks into smaller subnetworks, simplifying the study of frequency synchronization configurations.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- The Kuramoto model is a fundamental tool for studying synchronization in coupled oscillator networks.
- Analyzing synchronization in large, heterogeneous networks presents significant computational challenges due to complex nonlinear interactions.
Purpose of the Study:
- To develop a general framework for decomposing Kuramoto networks.
- To facilitate the study of frequency synchronization configurations in large, complex networks.
Main Methods:
- Utilizing homotopy deformation principles.
- Decomposing general Kuramoto networks into smaller, directed acyclic subnetworks.
Main Results:
- A novel framework for network decomposition is established.
- The framework enables a divide-and-conquer approach for analyzing synchronization.
Conclusions:
- The developed framework simplifies the analysis of frequency synchronization in large Kuramoto networks.
- This approach provides a foundation for studying complex synchronization behaviors in diverse network structures.
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