1. Validity of the phase approximation for coupled nonlinear oscillators: a case study
- Author
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Alessio Franci, Antoine Chaillet, William Pasillas-Lépine, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Neurosynch, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Pasillas-Lépine, William, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID
- Subjects
0209 industrial biotechnology ,[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] ,Phase (waves) ,[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS] ,Proportional control ,02 engineering and technology ,Synchronization ,01 natural sciences ,Phase locking ,Phase-models ,[SPI.AUTO]Engineering Sciences [physics]/Automatic ,Nonlinear oscillators ,Structural stability ,020901 industrial engineering & automation ,Control theory ,0103 physical sciences ,Statistical physics ,Small coupling ,010306 general physics ,Mathematics ,Kuramoto model ,Normal hyperbolicity ,[SPI.AUTO] Engineering Sciences [physics]/Automatic ,Phase dynamics ,Phase-locking - Abstract
International audience; Motivated by neuroscience applications, we rigorously derive the phase dynamics of an ensemble of interconnected nonlinear oscillators under the effect of a proportional feedback. We individuate the critical parameters determining the validity of the phase approximation and derive bounds on the accuracy of the latter in reproducing the behavior of the original system. We use these results to study the existence of oscillating phase-locked solutions in the original oscillator model.
- Published
- 2012