Coupled phase oscillators; Desynchronization; Euclidean spaces; Mean field; Phase oscillators; Control and Systems Engineering; Modeling and Simulation; Control and Optimization
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; Univ. Paris Sud 11, L2S - EECI - Supélec, 91192 Gif sur Yvette, France
Panteley, Elena; CNRS, L2S-Supélec, 91192 Gif sur Yvette, France
Chaillet, Antoine; Univ. Paris Sud 11, L2S - EECI - Supélec, 91192 Gif sur Yvette, France
Lamnabhi-Lagarrigue, Francoise; CNRS, L2S-Supélec, 91192 Gif sur Yvette, France
Language :
English
Title :
Desynchronization of coupled phase oscillators, with application to the Kuramoto system under mean-field feedback
Publication date :
2011
Event name :
IEEE Conference on Decision and Control and European Control Conference
Event place :
Usa
Event date :
12-12-2011 => 15-12-2011
Main work title :
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Publisher :
Institute of Electrical and Electronics Engineers Inc.
D. Aeyels and J. A. Rogge. Existence of partial entrainment and stability of phase locking behavior of coupled oscillators. Progress of Theoretical Physics, 112(6):921-942, 2004.
N. P. Bhatia and G. P. Szegö. Stability theory of dynamical systems. Die Grundlehren der mathematischen Wissenschaften, Band 161. Springer-Verlag, New York, 1970.
I.I. Blekhman, A.L. Fradkov, H. Nijmeijer, and A.Y. Pogromsky. On self synchronization and controlled synchronization. Syst. & Contr. Letters, 31:299-305, 1997.
E. Brown, P. Holmes, and J. Moehlis. Globally coupled oscillator networks. In Perspectives and problems in nonlinear science: A celebratory volume in honor of Larry Sirovich, pages 183-215, 2003.
G. Chen. Chaotification via feedback: The discrete case. In Lecture Notes in Control and Information Sciences, volume 292. Springer, 2003.
G. Chen and L. Yang. Chaotifying a continuous-time system near a stable limit cycle. Chaos, Solitons and Fractals, 15(2):245-253, 2003.
N. Chopra and M. W. Spong. On exponential synchronization of Kuramoto oscillators. IEEE Trans. on Automat. Contr., 54(2):353-357, 2009.
F. Dörfler and F. Bullo. Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators. IEEE Trans. on Automat. Contr., 2011. (submitted).
A. Franci, A. Chaillet, and S. Bezzaoucha. Toward oscillations inhibition by mean-field feedback in Kuramoto oscillators. In Proc. IFAC World Congress, Milan, Italy, August 2011.
A. Franci, A. Chaillet, E. Panteley, and F. Lamnabhi-Lagarrigue. Desynchronization and inhibition of all-to-all interconnected Kuramoto oscillators by scalar mean-field feedback. Mathematics of Control, Signals, and Systems - Special Issue on large-scale nonlinear systems, 2011. Submitted.
A. Franci, A. Chaillet, and W. Pasillas-Lépine. Existence and robustness of phase-locking in coupled Kuramoto oscillators under mean-field feedback. Automatica - Special Issue on Biology Systems, 47(6):1193-1202, 2010. Regular paper. Extended version available at: http://hal.archives-ouvertes.fr/ hal-00526066/.
A. Franci, A. Chaillet, and W. Pasillas-Lépine. Robustness of phase-locking between Kuramoto oscillators to time-varying inputs. In Proc. IFAC World Congress, Milan, Italy, August 2011.
Y. Gao and K. Chau. Chaotification of permanent-magnet synchronous motor drives using time-delay feedback. In IEEE Annual Conf. of Industrial Electronics Soc., pages 762-766, 2002.
J.K. Hale. Ordinary Differential equations. Interscience. John Wiley, New York, 1969.
A. Jadbabaie, N. Motee, and M. Barahona. On the stability of the Kuramoto model of coupled nonlinear oscillators. Proc. American Control Conf., pages 4296-4301, 2004.
Y. Kuramoto. Chemical Oscillations, Waves, and Turbulence. Springer, Berlin, 1984.
J. Lopez-Azcarate, M. Tainta, M. C. Rodriguez-Oroz, M. Valencia, R. Gonzalez, J. Guridi, J. Iriarte, J. A. Obeso, J. Artieda, and M. Alegre. Coupling between beta and high-frequency activity in the human subthalamic nucleus may be a pathophysiological mechanism in Parkinsons disease. J. Neurosci., 30(19):6667-6677, 2010.
V.V. Nemytskii and V.V. Stepanov. Qualitative theory of differential equations. Dover Publications, INC., New York. Reprint. Originally published: Princeton University Press, 1960.
R. Orsi, L. Praly, and I. Mareels. Sufficient conditions for the existence of an unbounded solution. Automatica, 37(10):1609-1617, 2001.
A. Pikovsky, M. Rosenblum, and J. Kurths. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge Nonlinear Science Series, Cambridge, United Kingdom, 2001.
D. Plenz and S. T. Kital. A basal ganglia pacemaker formed by the subthalamic nucleus and external globus pallidus. Nature, 400(6745):677-682, 1999.
K. Pyragas, O. V. Popovich, and P. A. Tass. Controlling synchrony in oscillatory networks with a separate stimulation-registration setup. EPL, 80(4), 2008.
M. Rosa, S. Marceglia, D. Servello, G. Foffani, L. Rossi, M. Sassi, S. Mrakic-Sposta, R. Zangaglia, C. Pacchetti C, M. Porta, and A. Priori. Time dependent subthalamic local field potential changes after DBS surgery in Parkinson's disease. Experimental Neurology, 222(2):184-190, 2010.
S. V. Sarma, M. Cheng, Z. Williams, R. Hu, E. Eskandar, and E. N. Brown. Comparing healthy and Parkinsonian neuronal activity in sub-thalamic nucleus using point process models. IEEE Trans Biomed Eng., 57(6):1297-1305, 2010.
S. H. Strogatz. From Kuramoto to Crawford: Exploring the onset of synchronization in population of coupled oscillators. Physica D, 143:1-20, 2000.
J. Volkmann, M. Joliot, A. Mogilner, A. A. Ioannides, F. Lado, E. Fazzini, U. Ribary, and R. Llinás. Central motor loop oscillations in Parkinsonian resting tremor revealed by magnetoencephalography. Neurology, 46:1359-1370, 1996.
O. V. Popovych, C. Hauptmann, and P. A. Tass. Desynchronization and decoupling of interacting oscillators by nonlinear delayed feedback. Internat. J. Bifur. Chaos, 16(7):1977-1987, 2006.
H. Zhang, D. Liu, and Z. Wang. Controlling Chaos: Suppression, Synchronization and Chaotification. Communications and Control Engineering. Springer-Verlag, 2009.