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Topological Control of Synchronization Patterns: Trading Symmetry for Stability
Joseph D Hart1,2, Yuanzhao Zhang3, Rajarshi Roy1,2,4
1Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.
Physical Review Letters
|March 2, 2019
Summary
Breaking network symmetry enhances synchronization stability in identical systems. This counterintuitive finding applies to various dynamics and network structures, offering new control possibilities.
Area of Science:
- Complex networks
- Nonlinear dynamics
- Synchronization phenomena
Background:
- Network symmetry often enhances synchronization stability.
- Identical synchronization is crucial in many coupled systems.
- Understanding symmetry's role is key to controlling network dynamics.
Purpose of the Study:
- To investigate the impact of structural symmetry on network synchronizability.
- To demonstrate that breaking symmetry can enhance synchronization.
- To explore applications in topological control of synchronization.
Main Methods:
- Theoretical analysis of network synchronizability.
- Numerical simulations for generic node dynamics and network structures.
- Experimental validation using a state-of-the-art optoelectronic system.
- Development of an optimization algorithm for cluster structures.
Main Results:
- Breaking structural symmetry enhances synchronizability for most symmetry clusters.
- This effect is robust across different node dynamics and network topologies.
- Experimental results confirm the theoretical predictions.
- An algorithm was developed to optimize cluster structures for enhanced synchronization.
Conclusions:
- Structural symmetry breaking is a powerful tool to improve network synchronizability.
- This finding challenges conventional understanding and opens new avenues for network control.
- The developed algorithm provides a practical method for optimizing network synchronization.
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