# Stability of twisted states on lattices of Kuramoto oscillators

@inproceedings{Goebel2021StabilityOT, title={Stability of twisted states on lattices of Kuramoto oscillators}, author={M. Goebel and Matthew S. Mizuhara and S. Stepanoff}, year={2021} }

Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying network topology and the emergent dynamics remains a rich area of investigation for both theory and experiment. In this work we study lattices of coupled Kuramoto oscillators with non-local interactions. Our focus is on the stability of twisted states. These are equilibrium solutions with constant phase shifts between… Expand

#### References

SHOWING 1-10 OF 43 REFERENCES

Twisted States in a System of Nonlinearly Coupled Phase Oscillators

- Physics
- Regular and Chaotic Dynamics
- 2019

We study the dynamics of the ring of identical phase oscillators with nonlinear nonlocal coupling. Using the Ott–Antonsen approach, the problem is formulated as a system of partial derivative… Expand

Small-world networks of Kuramoto oscillators

- Mathematics, Physics
- 2014

Two complementary approaches for studying q -twisted states in the coupled oscillator model on SW graphs are developed: linear stability analysis and numerical continuation, which show that long-range random connections in the SW graphs promote synchronization and yields the estimate of the synchronization rate as a function of the SW randomization parameter. Expand

Multistability of twisted states in non-locally coupled Kuramoto-type models.

- Mathematics, Medicine
- Chaos
- 2012

It is shown that the number of different stable multi-twisted states grows exponentially as N → ∞, and it is possible to interpret the equilibrium points of the coupled phase oscillator network as trajectories of a discrete-time translational dynamical system where the space-variable plays the role of time. Expand

Bifurcations in the Kuramoto model on graphs.

- Mathematics, Physics
- Chaos
- 2018

This work studies several model problems illustrating the link between network topology and synchronization in coupled dynamical systems, and identifies several families of graphs for which the transition to synchronization in the Kuramoto model starts at the same critical value of the coupling strength and proceeds in a similar manner. Expand

Partially coherent twisted states in arrays of coupled phase oscillators.

- Physics, Medicine
- Chaos
- 2014

It is found that stable twisted states with different wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario andSimulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system. Expand

Persistent clusters in lattices of coupled nonidentical chaotic systems.

- Mathematics, Medicine
- Chaos
- 2003

Analytical and numerical studies allow us to conclude that these cluster synchronization regimes persist when the chaotic oscillators have slightly different parameters, and they are stable and robust against up to 10%-15% parameter mismatch and against small noise. Expand

Cluster Synchronization in Three-Dimensional Lattices of Diffusively Coupled oscillators

- Mathematics, Computer Science
- Int. J. Bifurc. Chaos
- 2003

The appearance and order of stabilization of the cluster synchronization modes with increasing coupling between the oscillators are revealed for 2-D and 3-D lattices of coupled Lur'e systems and of coupled Rossler oscillators. Expand

From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

- Physics
- 2000

The Kuramoto model describes a large population of coupled limit-cycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certain… Expand

The Critical Properties of Two-dimensional Oscillator Arrays

- Physics
- 2008

We present a renormalization group study of two-dimensional oscillator arrays, with dissipative, short-range interactions. We consider the case of non-identical oscillators, with distributed… Expand

Phase synchronization in the two-dimensional Kuramoto model: Vortices and duality.

- Medicine
- Physical review. E
- 2021

A duality transformation similar to that carried out for the XY model of planar spins on the Hamiltonian version of the Kuramoto model is carried out to expose the underlying vortex structure. Expand