A minimal model of partial synchrony

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 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.

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Cited by in corpus (16)

• Chimera states in a multilayer network of coupled and uncoupled neurons
• Phase reduction beyond the first order: the case of the mean-field complex Ginzburg-Landau equation
• Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks
• Dynamics of a large system of spiking neurons with synaptic delay
• Connecting empirical phenomena and theoretical models of biological coordination across scales
• Solitary States and Partial Synchrony in Oscillatory Ensembles with Attractive and Repulsive Interactions
• Transition to Collective Oscillations in Finite Kuramoto Ensembles
• From phase to amplitude oscillators
• On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators
• Noise-induced stabilization of collective dynamics
• Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions
• Analytical Phase Reduction for Weakly Nonlinear Oscillators
• Irregular collective dynamics in a Kuramoto-Daido system
• Quasi phase reduction of all-to-all strongly coupled $\lambda -\omega$ oscillators near incoherent states
• Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic coupling
• Using Phase Dynamics to Study Partial Synchrony: Three Examples