Here, the Euler method of numerical integration is used to implement a basic Kuramoto model, $\dot{\theta}_i = \omega + \sum_{j=i-k_c}^{i+k_c} \sin (\theta_j - \theta_i)$, in pure JavaScript (using JQuery and Google Charts). Given an initial condition, $\theta_i(t)$, as the position of oscillator $i$ at time $t$, the next position of oscillator $i$ is obtained using

\begin{align*} \theta_i(t + h) & = \theta_i(t) + h \cdot \sum_{j=i - k_c}^{i + k_c} \sin [\theta_j(t) - \theta_i(t)] \end{align*}

where $h$ is the time step. One of the matters of interest in this thesis is what the locations of the oscillators relative to each other are after a long time i.e. after the network is deemed to be stable.

Note: Hover on buttons for tool tips about their functions. E.g. press "create" to load internally set network, press "load" to set your own network, press "play" to view simulation, press "pause" to pause simulation, etc. Enable the "manual" option in the Network Set-Up" setting to step through the simulation and set your own coupling number after enabling the coupling number checkbox.