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Phase resetting for a network of oscillators via phase response curve approach

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Abstract

The problem of phase regulation for a population of oscillating systems is considered. The proposed control strategy is based on a phase response curve (PRC) model of an oscillator (the first-order reduced model obtained for linearized system and inputs with infinitesimal amplitude). It is proven that the control provides phase resetting for the original nonlinear system. Next, the problem of phase resetting for a network of oscillators is considered when applying a common control input. Performance of the obtained solutions is demonstrated via computer simulation for three different models of circadian/neural oscillators.

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Authors and Affiliations

  1. Non-A project @ Inria, Parc Scientifique de la Haute Borne, 40 avenue Halley, 59650, Villeneuve d’Ascq, France

    D. Efimov

  2. LAGIS UMR 8219, Ecole Centrale de Lille, Avenue Paul Langevin, 59651, Villeneuve d’Ascq, France

    D. Efimov

  3. Department of Control Systems and Informatics, University ITMO, 49 avenue Kronverkskiy, 197101, Saint Petersburg, Russia

    D. Efimov

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  1. D. Efimov
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Correspondence to D. Efimov.

Additional information

This work was partially supported by the Government of Russian Federation (Grant 074-U01) and the Ministry of Education and Science of Russian Federation (Project 14.Z50.31.0031).

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Efimov, D. Phase resetting for a network of oscillators via phase response curve approach. Biol Cybern 109, 95–108 (2015). https://doi.org/10.1007/s00422-014-0629-z

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  • DOI: https://doi.org/10.1007/s00422-014-0629-z

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