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Type: Journal article
Title: Conformist-contrarian interactions and amplitude dependence in the Kuramoto model
Author: Lohe, M.
Citation: Physica Scripta, 2014; 89(11):115202-1-115202-10
Publisher: IOP
Issue Date: 2014
ISSN: 0031-8949
Statement of
M A Lohe
Abstract: We derive exact formulas for the frequency of synchronized oscillations in Kuramoto models with conformist–contrarian interactions, and determine necessary conditions for synchronization to occur. Numerical computations show that for certain parameters repulsive nodes behave as conformists, and that in other cases attractive nodes can display frustration, being neither conformist nor contrarian. The signs of repulsive couplings can be placed equivalently outside the sum, as proposed in Hong and Strogatz (2011 Phys. Rev. Lett. 106 054102), or inside the sum as in Hong and Strogatz (2012 Phys. Rev. E 85 056210), but the two models have different characteristics for small magnitudes of the coupling constants. In the latter case we show that the distributed coupling constants can be viewed as oscillator amplitudes which are constant in time, with the property that oscillators of small amplitude couple only weakly to connected nodes. Such models provide a means of investigating the effect of amplitude variations on synchronization properties.
Keywords: synchronization; Kuramoto model; amplitude dependence
Rights: © 2014 The Royal Swedish Academy of Sciences
RMID: 0030015596
DOI: 10.1088/0031-8949/89/11/115202
Appears in Collections:Physics publications

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