Linear reformulation of the Kuramoto model: Asymptotic mapping and stability properties

2nd International Conference on Communications Computing and Control Applications, CCCA 2012

Volumn , Issue , 2012, Pages

  Conteville, Laurie ^a   Panteley, Elena ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

ALL TO ALLS; COUPLED NONLINEAR OSCILLATORS; DIVERSE FIELDS; INITIAL CONDITIONS; KURAMOTO MODELS; LIMIT CYCLE; MODEL MAPS; PHASE LOCKED; STABILITY PROPERTIES;

LINEAR SYSTEMS; STABILITY;

MATHEMATICAL MODELS;

EID: 84874160281     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCCA.2012.6417871     Document Type: Conference Paper

References (23)

1. J.A. Acebron, L.L. Bonilla, C. J. Perez Vicente, F. Ritort, R. Spigler, "The Kuramoto model: a simple paradigm for synchronization phenomena". Rev. Mod. Phys. 77, 137-185 (2005).
2. R. M. Olfati-Saber, R.; Murray, Consensus Problems in Net-works of Agents with Switching Topology and Time-Delays, Automatic Control, IEEE Transactions on E 49E 1520-1533E (2004
3. G. F. R. Chris Godsi, Algebraic Graph Theory, 2001
4. M. Fiedler. Algebraic connectivity of graphs. Czechoslovak Mathematical Journal, 23(2): 298-305, 1973.
5. Y. Kuramoto, Cooperative Dynamics of Oscillator Commu-nity, Prog. Theor. Phys. Supplement No.79 (1984) pp. 223-240
6. Strogatz S.H., From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D, Volume 143, Number 1, 1 September 2000 , pp. 1-20.
7. S. H. Strogatz and R. E. Mirollo, Stability of incoherence in a population of coupled oscillators, J. Stat. Phys. 63 (1991).
8. P. C. Matthews, R. E. Mirollo, S. H. Strogatz, Dynamics of a large system of coupled nonlinear oscillators, Physica D: Nonlinear Phenomena, vol. 52, 1991, pp. 293-331.
9. P. C. Matthews, S. H. Strogatz, Phase diagram for the col-lective behavior of limit-cycle oscillators, Phys. Rev. Lett. 65, 1701-1704 (1990).
10. N. B. M. Jadbabaie, A.; Motee,-OOn the stability of the kuramoto model of coupled nonlinear oscillators,-O American Control Conference, vol. 5, pp. 4296-4301, 2004.
11. N. Chopra and M. W. Spong,-OOn exponential synchroniza-tion of kuramoto oscillators,-O IEEE TAC, vol. 54, no. 2, pp. 353-357, 2009.
12. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1987.
13. C. W. Wu. On a matrix inequality and its application to the synchronization in coupled chaotic systems. Com-plex Computing-Networks: Brain-like andWave-oriented Elec-trodynamic Algorithms, Springer Proceedings in Physics. 104:279-288, 2006.
14. D Aeyels, JA Rogge, Existence of partial entrainment and sta-bility of phase locking behavior of coupled oscillators, Progress of Theoretical Physics, 2004
15. D Aeyels, JA Rogge, Stability of phase locking in a ring of unidirectionally coupled oscillators, J. Phys. A, 37, 2004.
16. M. Verwoerd, O Mason, Global phase-locking in-nite popula-tions of phase-coupled oscillators, SIAM J. Appl. Dyn. Syst., 2008
17. M. Verwoerd, O Mason, On Computing the Critical Coupling Coe-cient for the Kuramoto Model on a Complete Bipartite Graph, SIAM J. Appl. Dyn. Syst., 8(1), 417-453, 2009.
18. R. Sepulchre, D. A. Paley, and N. E. Leonard,Stabiliza-tion of planar collective motion: All-to-all communication, IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 811-824, 2007.
19. A. Franci, A. Chaillet and W. Pasillas-L }Opine, Existence and robustness of phase-locking in coupled Kuramoto oscillators under mean-eld feedback, Automatica, 47, 1193-1202, 2011
20. G. Thut and Minussi, New insight into rhythmic brain activity from TMS-EEG studies, Trends Cognit. Sci. E 13 E 182-189 E (2009
21. DC Roberts, Linear reformulation of the Kuramoto model of self-synchronizing coupled oscillators, Physical Review E, 2008
22. F Dorer, F Bullo, Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators, SIAM J. Control Optim., 50(3), 1616-1642, 2012.
23. F Dorer, F Bullo, On the Critical Coupling for Kuramoto Oscillators, SIAM J. Appl. Dyn. Syst., 10(3), 1070-1099, 2011.