Group synchrony, parameter mismatches, and intragroup connections
Shirin Panahi1, Francesco Sorrentino1
1University of New Mexico, Albuquerque New Mexico 87106, USA.
Physical Review. E
|December 24, 2021
Summary
Stable group synchronization in complex networks is possible even with approximate conditions. This study analyzes stability and synchronization error, extending results for networks with intragroup connections.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- Group synchronization occurs when multiple distinct synchronization patterns coexist in oscillator networks.
- Previous studies characterized group synchronization under strict conditions of identical systems and precise couplings.
- Deviations from these ideal conditions often lead to a loss of synchronization.
Purpose of the Study:
- To investigate the stability of group synchronization when system parameters and couplings deviate slightly from nominal values.
- To analyze the impact of approximate conditions on the robustness of group synchronization.
- To extend the understanding of group synchronization stability to networks with intragroup connections.
Main Methods:
- Utilized the master stability function approach to derive necessary and sufficient conditions for stability.
- Quantified synchronization error arising from parameter and coupling deviations.
- Extended existing stability analysis to include intragroup connections within the network.
Main Results:
- Demonstrated that stable group synchronization can persist despite small deviations in system parameters and couplings.
- Provided a quantitative measure of synchronization error using the master stability function.
- Identified a broader class of intragroup connection matrices that simplify stability analysis.
Conclusions:
- Group synchronization is more robust to parameter and coupling variations than previously assumed.
- The master stability function provides a powerful tool for analyzing synchronization stability and error in complex networks.
- The study offers new insights into network structures that facilitate stable group synchronization, particularly with intragroup connections.
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