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Synched is a software tool designed to visualize synchronization phenomena in complex systems and networks. It includes the capability for displaying the real-time dynamics of several different models, including the Kuramoto model and several of its variations. Synched has been designed for use by a range of expertise, from students exploring dynamical systems for the first time, to expert researchers who have spent years studying such systems.


Creative Commons License
Synched by Per Sebastian Skardal is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

How to Use Synched
Below is a snapshot of Synched in action. The window is divided into two parts: the display on the left and the control panel on the right. The details of each are described below. Synched also has the capability of simulating several different models. For a description of all these models and some references, see the model description.

Synched displays the dynamics of the system in an outer circle and an inner circle. Additionally, if the Display info. box is checked information such as the model and degree of synchrony above and below.

Around the outer circle Synched plots each individual oscillator as a small circle. Each oscillator moves according to its own equation. If the Show Colors box is checked, then individual oscillators are color-coded, depending on the current model. For instance, for the Kuramoto model locked oscillators are colored yellow and drifting oscillators are colored red.

In the inner circle Synched displays the order parameter(s) for the current model. The order parameter(s) describe the macroscopic dynamics of all the oscillators and describe the degree of synchrony of the system. If the order parameter(s) is near zero, i.e., close to the origin, then the system is incoherent. If the order parameter(s) is larger, i.e., closer to the circle, then the system is synchronized. The larger the order parameter(s), the more synchronized the system. For more information on the order parameter(s) for different models, see the model description.

Control Pannel:
Master Controls:

Model allows you to change the model you'd like to simulated for your next simulation. You can choose between Kuramoto, Bimodal, Time-Delayed, Clusters, and Communities. For more details on these models see the model description.

# Oscillators allows you to change the size of your next simulation. You can choose between 49, 100, 400, or 900 oscillators.

New Simulation resets the system to the model and # of oscillators you have chosen.

Parameter Controls: (depending on the model you are using, only some of the parameters can be used.)

k changes the local coupling strength, i.e., the coupling strength between oscillators in the same community. This parameter is only used in the communities model.

K changes the global coupling strength of the system.

Mean Frequency changes the average frequency of all the oscillators. In the Bimodal model it changes the distance between peaks of the two halves of the frequency distribution.

Cluster q changes the clustering integer defining the coupling function. This parameter is only used in the Clusters model.

Forcing F changes the strength of forcing that can be applied to the system. To force oscillators towards an angle, click and hold on a point on the display corresponding to the angle.

Display Controls:

Display Info. toggles the information display visible/invisible.

Show Colors toggle the color option on/off.

Pause pauses the simulation.

Speed changes the speed of the simulation.

Quit closes Synched.