# Kuramoto dynamics in Hamiltonian systems.

@article{Witthaut2014KuramotoDI, title={Kuramoto dynamics in Hamiltonian systems.}, author={Dirk Witthaut and Marc Timme}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2014}, volume={90 3}, pages={ 032917 } }

The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We show that locking of the phase of one oscillator on a Kuramoto manifold to the average phase emerges… Expand

#### 28 Citations

Topaj–Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators

- Physics
- Regular and Chaotic Dynamics
- 2019

We discuss the Hamiltonian model of an oscillator lattice with local coupling. The Hamiltonian model describes localized spatial modes of nonlinear the Schrödinger equation with periodic tilted… Expand

Dynamics of phases and chaos in models of locally coupled conservative or dissipative oscillators.

- Physics
- 2019

We discuss Hamiltonian model of oscillator lattice with local coupling. Model describes spatial modes of nonlinear Schrodinger equation with periodic tilted potential. The Hamiltonian system… Expand

Occasional uncoupling overcomes measure desynchronization.

- Physics, Medicine
- Chaos
- 2018

It is illustrated that as a coupled system evolves in time, occasionally switching off the coupling when the system is in the measure desynchronized state can bring the system back in measure synchrony. Expand

Cycle flows and multistability in oscillatory networks.

- Physics, Medicine
- Chaos
- 2017

This work establishes the existence of geometrically frustrated states in networks of phase oscillators-where although a steady state flow pattern exists, no fixed point exists in the dynamical variables of phases due to geometrical constraints and describes the stable fixed points of the system in terms of cycle flows. Expand

Classical discrete time crystals

- Physics
- 2018

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective… Expand

Linearization error in synchronization of Kuramoto oscillators

- Computer Science
- Appl. Math. Comput.
- 2021

It is proved that if a globally coupled network with frustration has perfect phase synchronization when its coupling strength tends to infinity, it is a regular network and a mathematical framework to estimate errors of the linear approximation for globally and locally coupled networks is developed. Expand

Synchronization in an evolving network

- Computer Science, Physics
- 2015

The dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution is studied, finding the synchronous state remains stable as long as the connection density remains above the threshold value. Expand

Controlling and enhancing synchronization through adaptive phase lags.

- Medicine, Physics
- Physical review. E
- 2019

The threshold for instability for the adaptive lag model shows robustness against variations in the associated time constant down to lower densities of controlled oscillators and a simple intuitive model emerges based on the interaction between splayed clusters close to a critical point. Expand

Fisher information and criticality in the Kuramoto model of nonidentical oscillators.

- Mathematics, Medicine
- Physical review. E
- 2018

It is shown across a range of topologies that the Fisher information peak points to a transition for smaller graphs that indicates structural changes in the numbers of locally phase-synchronized clusters, often directly from metastable to stable frequency synchronization. Expand

A two-frequency-two-coupling model of coupled oscillators.

- Medicine, Physics
- Chaos
- 2021

The simplicity of the model promises that real-world systems can be found which display the dynamics induced by correlated/uncorrelated disorder, and Numerical simulations performed on the model show good agreement with the analytic predictions. Expand

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