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SYNCHRONIZATION OF HETEROGENEOUS OSCILLATORS UNDER NETWORK MODIFICATIONS: PERTURBATION AND OPTIMIZATION OF THE
Dane Taylor1, Per Sebastian Skardal2, Jie Sun3
1Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA; and Statistical and Applied Mathematical Sciences Institute (SAMSI), Research Triangle Park, NC, 27709, USA.
SIAM Journal on Applied Mathematics
|November 23, 2016
Summary
This study introduces a synchrony alignment function (SAF) to optimize network synchronization in complex systems. It uses spectral analysis and gradient descent to modify network structures for enhanced synchronization, crucial for engineering and biology.
Area of Science:
- Complex systems
- Network science
- Dynamical systems theory
Background:
- Synchronization is critical in diverse systems like power grids, biological rhythms, and electronic circuits.
- Understanding how to control synchronization through network adaptation is a significant challenge.
- Real-world systems often exhibit heterogeneous node dynamics, complicating synchronization.
Purpose of the Study:
- To investigate the impact of network modifications on synchronization in systems with heterogeneous dynamics.
- To develop a quantitative measure for assessing a system's synchronizability.
- To create efficient algorithms for optimizing network structure to enhance synchronization.
Main Methods:
- Development of a synchrony alignment function (SAF) to quantify synchrony.
- Spectral perturbation analysis of the SAF for structural network changes (edge addition/removal).
- Gradient-descent algorithms for optimizing network modifications to maximize phase synchronization.
Main Results:
- The SAF effectively measures the interplay between network and oscillator heterogeneity.
- Spectral analysis identifies critical network edges for synchronization control.
- Optimized network modifications significantly enhance phase synchronization.
Conclusions:
- Network structure plays a pivotal role in controlling synchronization in heterogeneous systems.
- The SAF and developed algorithms provide a powerful framework for engineering and adapting complex networks.
- This research offers insights into enhancing or inhibiting synchronization for improved system functionality.
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