Coupled nonlinear oscillators; Non-linear oscillators; Original systems; Oscillating phase; Oscillator model; Phase approximations; Phase dynamics; Proportional feedback; 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 - Supélec, Gif sur Yvette 91192, France
Pasillas-Lepine, William; CNRS - L2S, France
Chaillet, Antoine; L2S - Univ. Paris Sud 11 - Supélec, France
Language :
English
Title :
Validity of the phase approximation for coupled nonlinear oscillators: A case study
Publication date :
2012
Event name :
2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
Event place :
Usa
Event date :
10-12-2012 => 13-12-2012
Journal title :
IEEE Conference on Decision and Control
ISSN :
0743-1546
eISSN :
2576-2370
Publisher :
Institute of Electrical and Electronics Engineers Inc.
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Bibliography
A. T. Winfree, The geometry of biological times. New-York: Springer, 1980.
K. Wiesenfeld, P. Colet, and S. H. Strogatz, "Synchronization transitions in a disordered Josephson series array," Phys. Rev. Lett., vol. 76, 1996.
L. Scardovi, A. Sarlette, and R. Sepulchre, "Synchronization and balancing on the N-torus," Syst. & Contr. Letters, vol. 56, no. 5, pp. 335-341, 2007.
F. Dorfler and F. Bullo, "On the critical coupling for Kuramoto oscillators," SIAM Journal on Applied Dynamical Systems, vol. 10, no. 3, pp. 1070-1099, 2011.
A. Pavlov, N. van de Wouw, and H. Nijmeijer, Uniform output regulation of nonlinear systems: a convergent dynamics approach, ser. Systems and controls: foundations and applications. Boston: Birkhauser, 2006.
N. Chopra and M. W. Spong, "On exponential synchronization of Kuramoto oscillators," IEEE Trans. on Automat. Contr., vol. 54, no. 2, pp. 353-357, 2009.
A. Papachristodoulou and A. Jadbabaie, "Synchonization in oscillator networks with heterogeneous delays, switching topologies and nonlinear dynamics," in Proc. 45th. IEEE Conf. Decision Contr., 2006, pp. 4307-4312.
D. Aeyels and J. A. Rogge, "Existence of partial entrainment and stability of phase locking behavior of coupled oscillators," Progress of Theoretical Physics, vol. 112, no. 6, pp. 921-942, 2004.
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, vol. 47, no. 6, pp. 1193-1202, 2010.
A. Franci, A. Chaillet, E. Panteley, and F. Lamnabhi-Lagarrigue, "Desynchronization and inhibition of kuramoto oscillators by scalar mean-field feedback," Mathematics of Control, Signals, and Systems (MCSS), pp. 1-49, 2012.
D. G. Aronson, G. B. Ermentrout, and N. Kopell, "Amplitude response of coupled oscillators," Physica D, vol. 41, no. 3, pp. 403-449, 1990.
J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, 7th ed., ser. Applied Mathematical Sciences. New-York: Springer, 2002, vol. 42.
F. C. Hoppensteadt and E. M. Izhikevich, Weakly connected neural networks, ser. Applied Mathematical Sciences. New York: Springer-Verlag, 1997, vol. 126.
D. V. Ramana Reddy, A. Sen, and G. L. Johnston, "Time delay induced death in coupled limit cycle oscillators," Physical Review Letters, vol. 80, no. 23, pp. 5109-5112, 1998.
W. Wang and J. J. E. Slotine, "On partial contraction analysis for coupled nonlinear oscillators," Biological cybernetics, vol. 92, no. 1, pp. 38-53, 2005.
A. Franci, W. Pasillas-Lèpine, and A. Chaillet, "Validity of the phase approximation for coupled nonlinear oscillators: a case study," 2012, Preprint. Available at: http://hal.archives-ouvertes.fr/hal-00727760.
M. Hirsch, C. Pugh, and M. Shub, Invariant Manifolds, ser. Lecture Notes in Mathematics. Berlin, Germany: Springer-Verlag, 1977.
G. B. Ermentrout and N. Kopell, "Oscillator death in systems of coupled neural oscillators," SIAM J. Appl. Math., vol. 50, no. 1, pp. 125-146, 1990.
J. Lee, Introduction to smooth manifolds, ser. Graduate Texts in Mathematics. Berlin, Germany: Springer-Verlag, 2006.
Y. Kuramoto, Chemical oscillations, waves, and turbulence. Berlin: Springer, 1984.
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