Multiplicity of singular synchronous states in the Kuramoto model of coupled oscillators
Related Experiment Video
Updated: May 5, 2026

Evaluation of Synaptic Multiplicity Using Whole-cell Patch-clamp Electrophysiology
Published on: April 23, 2019
Maxim Komarov1, Arkady Pikovsky
1Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Strasse 24, D-14476 Potsdam, Germany and Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
Abstract:
We study the Kuramoto model of globally coupled oscillators with a biharmonic coupling function. We develop an analytic self-consistency approach to find stationary synchronous states in the thermodynamic limit and demonstrate that there is a huge multiplicity of such states, which differ microscopically in the distributions of locked phases. These synchronous regimes already exist prior to the linear instability transition of the fully asynchronous state. In the presence of white Gaussian noise, the multiplicity is lifted, but the dependence of the order parameters on coupling constants remains nontrivial.
Related Concept Videos
Simplified Synchronous Machine Model
In this model, each generator is connected to a...
¹H NMR Signal Multiplicity: Splitting Patterns
Oscillations about an Equilibrium Position
Oscillations In An LC Circuit
State Space Representation
Consider an RLC circuit, a...
Spin–Spin Coupling Constant: Overview
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...

