A minimal model of partial synchrony

We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto-Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a uniform to distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of a inhomogeneous distribution. The characteristic and most peculiar property of partial synchrony is the difference between the frequencies of single units and that of the macroscopic field. PACS numbers: 05.45.Jn, 05.45.-a ar X iv :1 60 7. 07 17 8v 1 [ nl in .A O ] 2 5 Ju l 2 01 6 A minimal model of partial synchrony 2

[1]  Julia Kluge,et al.  Emergence Of Dynamical Order Synchronization Phenomena In Complex Systems , 2016 .

[2]  Antonio Politi,et al.  Equivalence of phase-oscillator and integrate-and-fire models. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Y. Kuramoto,et al.  Slow switching in globally coupled oscillators: robustness and occurrence through delayed coupling. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[5]  Vreeswijk,et al.  Partial synchronization in populations of pulse-coupled oscillators. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Hansel,et al.  Clustering and slow switching in globally coupled phase oscillators. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.