On the stability of the Kuramoto model of coupled nonlinear oscillators

• Published in: 2004 American Control Conference Proceedings; Volume 5 of 6 Vol. 5; pp. 4296 - 4301 vol.5
• Main Authors: Jadbabaie, A., Motee, N., Barahona, M.
• Format: Conference Proceeding Journal Article
• Language: English
• Published: Piscataway NJ IEEE 01.01.2004; Evanston IL American Automatic Control Council
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory; Control theory. Systems; Coupled mode analysis; Couplings; Educational institutions; Exact sciences and technology; Frequency synchronization; Graph theory; Network topology; Oscillators; Physics; Stability; Natural frequency; Interconnection network; Non linear oscillator; Uncertain system; Coupled oscillator; Spectral theory; Non linear model; Graph theory; Topology
• ISBN: 9780780383357; 0780383354
• ISSN: 0743-1619
• DOI: 10.23919/ACC.2004.1383983

We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We also provide a series of bounds for the critical values of the coupling strength.