# The size of the sync basin.

@article{Wiley2006TheSO, title={The size of the sync basin.}, author={Daniel A Wiley and Steven H. Strogatz and Michelle Girvan}, journal={Chaos}, year={2006}, volume={16 1}, pages={ 015103 } }

We suggest a new line of research that we hope will appeal to the nonlinear dynamics community, especially the readers of this Focus Issue. Consider a network of identical oscillators. Suppose the synchronous state is locally stable but not globally stable; it competes with other attractors for the available phase space. How likely is the system to synchronize, starting from a random initial condition? And how does the probability of synchronization depend on the way the network is connected… Expand

#### 183 Citations

The size of the sync basin revisited.

- Mathematics, Physics
- Chaos
- 2017

The equal-frequency Kuramoto model on a cycle is considered and it is found that the basin volumes scale as (1-4q/n)n, contrasting with the Gaussian behavior postulated in the study by Wiley et al. Expand

When is sync globally stable in sparse networks of identical Kuramoto oscillators?

- Computer Science, Physics
- Physica A: Statistical Mechanics and its Applications
- 2019

A partial answer to when the synchronized state is not globally stable is provided, if a graph allows a cyclic graph clustering with a sufficient number of clusters or contains a sufficiently long induced subpath without cut vertices of the graph then there is a non-synchronous stable phase-locked solution. Expand

On the Basin of Attractors for the Unidirectionally Coupled Kuramoto Model in a Ring

- Mathematics, Computer Science
- SIAM J. Appl. Math.
- 2012

We present the long-time dynamics of unidirectionally coupled identical Kuramoto oscillators in a ring, when each oscillator is influenced sinusoidally by a single preassigned oscillator. In this… Expand

Synchronization in time-varying networks.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is found that the time taken to reach synchronization is lowered and the stability range of the synchronized state increases considerably in dynamic networks, and so the linear stability analysis and the basin stability criterion provide complementary indicators of stability. Expand

Diversity enhanced synchronization in a small-world network of phase oscillators

- Physics, Mathematics
- 2019

In this work, we study the synchronization of a group of phase oscillators (rotors) in the small-world (SW) networks. The distribution of intrinsic angular frequency of the rotors are given by a… 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

Noise-induced desynchronization and stochastic escape from equilibrium in complex networks.

- Mathematics, Physics
- Physical review. E
- 2019

It is found that, quite counterintuitively, systems with inertia leave their initial basin faster than or at the same time as systems without inertia, except for strong white-noise perturbations. 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

Stability in the Kuramoto–Sakaguchi model for finite networks of identical oscillators

- Physics
- Nonlinear Dynamics
- 2019

We study the Kuramoto–Sakaguchi model composed by N identical phase oscillators symmetrically coupled. Ranging from local (one-to-one, \(R=1\)) to global (all-to-all, \(R=N/2\)) couplings, we derive… Expand

The Kuramoto Model on Power Law Graphs: Synchronization and Contrast States

- Physics, Computer Science
- J. Nonlinear Sci.
- 2020

It is shown that despite sparse connectivity, power law networks possess remarkable synchronizability: the synchronization threshold can be made arbitrarily low by varying the parameter of the power law distribution. Expand

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