Winner-take-all in a phase oscillator system with adaptation

We consider a system of generalized phase oscillators with a central element and radial connections. In contrast to conventional phase oscillators of the Kuramoto type, the dynamic variables in our system include not only the phase of each oscillator but also the natural frequency of the central osc...

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Bibliographic Details
Published in:Scientific reports 2018-01, Vol.8 (1), p.416-416, Article 416
Main Authors: Burylko, Oleksandr, Kazanovich, Yakov, Borisyuk, Roman
Format: Article
Language:English
Subjects:
631/378/116/1925
631/378/116/2393
639/705/1041
Humanities and Social Sciences
Mathematical models
multidisciplinary
Oscillators
Science
Science (multidisciplinary)
Synchronization
Take-all disease
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Summary:We consider a system of generalized phase oscillators with a central element and radial connections. In contrast to conventional phase oscillators of the Kuramoto type, the dynamic variables in our system include not only the phase of each oscillator but also the natural frequency of the central oscillator, and the connection strengths from the peripheral oscillators to the central oscillator. With appropriate parameter values the system demonstrates winner-take-all behavior in terms of the competition between peripheral oscillators for the synchronization with the central oscillator. Conditions for the winner-take-all regime are derived for stationary and non-stationary types of system dynamics. Bifurcation analysis of the transition from stationary to non-stationary winner-take-all dynamics is presented. A new bifurcation type called a Saddle Node on Invariant Torus (SNIT) bifurcation was observed and is described in detail. Computer simulations of the system allow an optimal choice of parameters for winner-take-all implementation.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-017-18666-3