kuramoto-2d

Kuramoto lattice model in Python and julia

To cite this code, please use:

This repo contains implementations of the Kuramoto coupled oscillator model on a 2D lattice.
The code is available in Python and Julia.

Ref.: Acebrón, J.A., Bonilla, L.L., Pérez Vicente, C.J., Ritort, F., Spigler, R., The Kuramoto model: A simple paradigm for synchronization phenomena. Rev Mod Phys 77(1):137-185, 2005.

Rendered page: https://frederic-vw.github.io/kuramoto-2d/

Python Requirements:

1. python installation, latest version tested 3.6.9
2. python packages (pip install package-name)
   • NumPy
   • Matplotlib
   • SciPy
   • opencv-python (save data as movie)

Julia Requirements:

1. julia installation, latest version tested 1.6.1
2. julia packages (julia > using Pkg; Pkg.add("Package Name"))
   • Interpolations
   • NPZ
   • PyCall (load Matplotlib animation functionality)
   • PyPlot
   • Statistics
   • VideoIO (save data as movie)

Kuramoto model

The Kuramoto lattice model is defined by:

Noise is added via stochastic integration:

The main function call running the simulation is: kuramoto2d(N, T, t0, dt, s, K0, K1, sd_omega):

• N: lattice size (N,N)
• T: number of simulation time steps
• t0: number of ‘warm-up’ iterations
• dt: integration time step
• s: noise intensity (σ)
• K0,K1: Kuramoto coupling constant (start, end values)

Outputs: (T,N,N) array as NumPy .npy format and as .mp4 movie.

Example-1

Parameters:
N = 128, T = 3000, t0 = 0, dt = 0.05, s = 0.2, K0 = 0.5, K1 = 4.0, sd_omega = 0.25

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