Go Back   Physics Help Forum > College/University Physics Help > Theoretical Physics

Theoretical Physics Theoretical Physics Help Forum

LinkBack Thread Tools Display Modes
Old Apr 10th 2019, 05:12 AM   #1
Junior Member
Join Date: Apr 2019
Posts: 1
Thumbs up 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.
Jakes is offline   Reply With Quote

  Physics Help Forum > College/University Physics Help > Theoretical Physics

computational, kuramoto, model, simulations, synchronization

Thread Tools
Display Modes

Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
moment for 3D model ling233 Kinematics and Dynamics 3 Oct 31st 2015 07:27 AM
model with mirror suvadip Light and Optics 1 Sep 10th 2013 09:38 AM
About a science model soumyadip_2k Thermodynamics and Fluid Mechanics 1 Oct 5th 2008 07:44 AM

Facebook Twitter Google+ RSS Feed