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 Theoretical Physics Theoretical Physics Help Forum Apr 10th 2019, 05:12 AM #1 Junior Member   Join Date: Apr 2019 Posts: 1 Simulations of Kuramoto Model I'm trying to understand and computationally model the Kuramoto Model. This is a mathematical model used to describe synchronization (phase locking of a set of $N$ oscillators). The governing equations: $$\frac{d \theta_i}{dt} = \omega_i + \frac{K}{N}\sum_{j=1}^{N}\sin(\theta_j - \theta_i)~~~~~~~~i=1...N$$ where the system is composed of $N$ oscillators, with phases $\theta_i$ and coupling $K$. As I understand, these phases $\theta_i$ refer to the respective phases of each oscillator. For an individual harmonic oscillator this would be $\phi$ in $$x(t) = A \cos(\omega t + \phi).$$ Consider this animation which shows various levels of phase locking by plotting the phases of the respective oscillators as a function of time. Question: I'm trying to find a viable numerical scheme used to produce this type of animation. Would it be viable to use the transformation $$re^{i \psi} = \frac{1}{N} \sum_{j=1}^{N}e^{\theta_j}$$ which allows a reformulation of the governing equations to $$\frac{d \theta_i}{d t} = \omega_i - Kr \sin(\theta_i).$$ As described in the wiki entry Kuramoto model. Then using some initial phase values $\theta_i$, together with the reformulated governing equations, we could map out the evolution of each individual phase as in the animation. Is this a viable numeric scheme for producing the animation which shows phase locking? Thanks for your assistance.  Tags computational, kuramoto, model, simulations, synchronization Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post ling233 Kinematics and Dynamics 3 Oct 31st 2015 07:27 AM suvadip Light and Optics 1 Sep 10th 2013 09:38 AM soumyadip_2k Thermodynamics and Fluid Mechanics 1 Oct 5th 2008 07:44 AM