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Abstract
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 distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of an inhomogeneous distribution. The characteristic and most peculiar property of self-consistent partial synchrony is the difference between the frequency of single units and that of the macroscopic field.
Highlights
Many physical systems can be represented as networks of oscillators, different examples ranging from the mammalian brain [1], to power grids [2], out-of-equilibrium chemical reactions [3], spin-torque nanoscale oscillators [4,5,6], gene-controlled clocks in bacteria [7], and so on
To further explore the ubiquity of self-consistent partial synchrony (SCPS), we study its emergence in an ensemble of linearly coupled Rayleigh oscillators
We find that more harmonics are needed to ensure that two-cluster states and the corresponding heteroclinic cycles (HCs) are both unstable
Summary
We analyze in detail appearance and stability properties of this state in possibly the this work must maintain attribution to the simplest setup of a biharmonic Kuramoto–Daido phase model as well as demonstrate the effect in author(s) and the title of the work, journal citation limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a and DOI. Uniform distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of an inhomogeneous distribution.
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