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Conference Papers Year : 2011

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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Dates and versions

hal-00652617 , version 1 (15-12-2011)

Identifiers

  • HAL Id : hal-00652617 , version 1

Cite

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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