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Synchronization in asymmetrically coupled networks with homogeneous oscillators.
1Nonlinear Dynamical Systems Group, Department of Mathematics, San Diego State University, San Diego, California 92182, USA.
Physical Review. E
|March 19, 2021
Summary
Stable synchronization in networks of identical coupled oscillators is possible even with asymmetric connections. This study mathematically proves previous findings incorrect, demonstrating stable synchronization in homogeneous networks.
Area of Science:
- Physics
- Network Science
- Dynamical Systems
Background:
- Synchronization is a common phenomenon in symmetrically coupled homogeneous oscillator networks.
- Recent studies suggested stable synchronization requires heterogeneous oscillators in asymmetrically coupled networks.
Purpose of the Study:
- To mathematically disprove the necessity of heterogeneous oscillators for stable synchronization in asymmetrically coupled networks.
- To demonstrate the existence of stable synchronization states in homogeneous, asymmetrically coupled oscillator systems.
Main Methods:
- Mathematical proof of synchronization conditions.
- Numerical simulations to validate theoretical findings.
Main Results:
- Stable synchronization states exist in asymmetrically coupled homogeneous oscillator networks.
- Previous conclusions regarding the necessity of heterogeneity for stable synchronization in such networks were mathematically incorrect.
Conclusions:
- Asymmetric coupling does not preclude stable synchronization in homogeneous oscillator networks.
- The study corrects and refines the understanding of synchronization phenomena in complex networks.
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