Abstract
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.
DOI
10.1038/s41598-017-18666-3
Publication Date
2018-01-11
Publication Title
Scientific Reports
Volume
8
Issue
1
Publisher
Springer Science and Business Media LLC
ISSN
2045-2322
Embargo Period
2024-11-22
Recommended Citation
Burylko, O., Kazanovich, Y., & Borisyuk, R. (2018) 'Winner-take-all in a phase oscillator system with adaptation', Scientific Reports, 8(1). Springer Science and Business Media LLC: Available at: https://doi.org/10.1038/s41598-017-18666-3
