Synchronization on fully connected graph with periodically switching edges

This applet visualizes synchronization of Kuramoto oscillators on fully connected graph with periodically switching edges. In order to run the applet you need Java Runtime Environment installed.

N : the number of Kuramoto oscillators.
K : coupling constant.
Ω : natural frequency of edge switching.
a : see Detail below.
Tmax : maximal simulation time.
Δ : phase order parameter [0,1].
ρ : edge density.

The thick orange-colored bar in the center shows the average global phase and the phase order parameter.

The button 'Init' makes all simulation setting initialize. 'd' sets the size of oscillator. The slider bar 'speed' controls simulation speed. The check box 'Edge' switches showing edges. The green dot in the ρ-Δ plot indicates current values of (ρ,Δ) at simulation time.
If the check box 'Random' is checked, instead of rule 2 in the Detail, node i and j are stochastically connected as preserving edge density at that time.

Detail)
1. The Kuramoto model consists of N coupled phase oscillators φi(t) having natural frequencies ωi. Here, ωi is distributed by Gaussian function with μ=0 and σ2=1. Their dynamics are governed by

dφi/dt=ωi+K/N Σj=1Nsin(φi-φj)


2. The oscillators are fully connected and each edge is periodically switched. If a edge between node i and j has a value, calculated by following equation, larger than 0, then node i and j are connected. Otherwise, they are disconnected. Here, θij is randomly selected from [0,aπ] and a=[1.0,2.0].

sin(Ωt+θij)

Reference) Sang Hoon Lee, Sungmin Lee, Seung-Woo Son, and Petter Holme, Phys. Rev. E 85, 027202 (2012) arXiv:1111.3734.
Contact) Sang Hoon Lee lshlj82@gmail.com, Sungmin Lee sungmin.lee@ntnu.no