Conformist–contrarian interactions and amplitude dependence in the Kuramoto model

M A Lohe
2014 Physica Scripta  
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 Phys.
more » ... roposed in Phys. Rev. Lett. 106 (2011) 054102, or inside the sum as in Phys. Rev. E 85 (2012) 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.
doi:10.1088/0031-8949/89/11/115202 fatcat:5xzgg75zy5fpph6xkryxmfy2cq