Constants of Motion in the Kuramoto Model

[thrillhouse86]

Hey All,

I realize this is a slightly peculiar question - but does anyone know if there is any conserved quantities in the Kuramoto Model. I've been thinking about it, and since the system is made up of coupled Limit Cycle Oscillators and there is no dissipation, wouldn't the total energy be conserved ?

The problem is that I cannot form the Lagrangian from the equations of motion for the life of me, has anyone dealt with this problem or can offer me any advice on how to try and form the Lagrangian ?

Thrillhouse86

 

[eljose79]

,

Thank you for your question. As a scientist studying the Kuramoto Model, I can confirm that there are indeed conserved quantities in this system. The total energy is one of them, as you mentioned. This is due to the fact that there is no dissipation in the system, so the energy is not lost over time.

In addition to energy, there are also other conserved quantities in the Kuramoto Model. These include the total phase and the total phase gradient. The total phase is the sum of all the individual phases of the oscillators, while the total phase gradient is the sum of the differences in the phases of adjacent oscillators.

As for forming the Lagrangian, it can be a challenging task for the Kuramoto Model due to its non-linear nature. One approach is to use the collective coordinates method, which involves approximating the dynamics of the system using a small number of variables. This can simplify the Lagrangian and make it easier to work with.

I hope this helps and good luck with your research!