This file describes the Synched software and includes citations to related works.

Synched is a piece of software that allows any user, ranging from a dynamical systems student exploring synchronization for the first time to a senior researcher presenting at a conference, to simulate and visualize in real time the phenomenon of synchronization using Kuramoto oscillators. Upon opening the application, a simulation of the standard all-to-all Kuramoto model begins, depicting oscillators as small circles moving along the outer circle according to their evolution ODE and an order parameter, describing the degree of synchronization, depicted by a larger circle in the middle. The natural frequencies are drawn from the Lorentzian distribution g(ω) = π-1/[1+(ω-ω0)2]. This software allows the user to tune both the global coupling strength and the mean frequency to explore the dynamics of the system and observe the phenomenon of synchronization in real time. For instance, when K becomes large enough, a subset of the population, i.e. oscillator that turn yellow, becomes phase-locked, representing a state of partial synchronization. The user can also increase the number of oscillators by choosing between system sizes of N = 49, 100, 400, or 900. Synched is for MacOSX and free to download and use for academic purposes at https://sites.google.com/site/persebastianskardal/software/synched.

In addition to the standard all-to-all Kuramoto model, the user can explore the effect of community structure, time-delays, and clustering by changing the model type. These models introduce more complexity into the system, and have more tunable parameters that the user can change in real time. The specifics of each model, as well as the relevant parameters and their interpretations, are described in detail on the website.