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Existence of phase-locking in the Kuramoto system under mean-fi eld feedback

Abstract : Motivated by the development of Deep Brain Stimulation (DBS) for neurological diseases, we study a network of interconnected oscillators under the influence of a proportional mean-fi eld feedback. Under standard assumptions, this system can be reduced to a modi fied version of the Kuramoto model of coupled nonlinear oscillators. In the first part of the paper we show that, in general, no oscillating phase-locked solution can co-exist with any non-zero feedback gain. In the second part we propose a new characterization of phase-locking between Kuramoto oscillators. In particular we derive a fi xed point equation for the Kuramoto system under mean- field feedback and we show how, generically, the "standard" (with zero feedback gain) Kuramoto fixed point equation is locally invertible in terms of the implicit function theorem.
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Contributor : Antoine Chaillet Connect in order to contact the contributor
Submitted on : Thursday, December 15, 2011 - 11:15:38 PM
Last modification on : Wednesday, September 16, 2020 - 4:44:55 PM
Long-term archiving on: : Friday, November 16, 2012 - 3:45:18 PM


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  • HAL Id : hal-00652617, version 1



Alessio Franci, William Pasillas-Lépine, Antoine Chaillet. Existence of phase-locking in the Kuramoto system under mean-fi eld feedback. IFAC World Congress, Aug 2011, Milan, Italy. pp.1-6. ⟨hal-00652617⟩



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