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- ItemNonuniversal transitions to synchrony in the Sakaguchi-Kuramoto model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Omel'chenko, Oleh; Wolfrum, MatthiasWe investigate the transition to synchrony in a system of phase oscillators that are globally coupled with a phase lag (Sakaguchi-Kuramoto model). We show that for certain unimodal frequency distributions there appear unusual types of synchronization transitions, where synchrony can decay with increasing coupling, incoherence can regain stability for increasing coupling, or multistability between partially synchronized states and/or the incoherent state can appear. Our method is a bifurcation analysis based on a frequency dependent version of the Ott-Antonsen method and allows for a universal description of possible synchronization transition scenarios for any given distribution of natural frequencies. ...
- ItemIs there an impact of small phase lags in the Kuramoto model?(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Omelchenko, Oleh; Wolfrum, MatthiasWe discuss the influence of small phase lags on the synchronization transitions in the Kuramoto model for a large inhomogeneous population of globally coupled phase oscillators. Without a phase lag, all unimodal distributions of the natural frequencies give rise to a classical synchronization scenario, where above the onset of synchrony at the Kuramoto threshold there is an increasing synchrony for increasing coupling strength. We show that already for arbitrarily small phase lags there are certain unimodal distributions of natural frequencies such that for increasing coupling strength synchrony may decrease and even complete incoherence may regain stability. Moreover, our example allows a qualitative understanding of the mechanism for such non-universal synchronization transitions