One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes
- Gupta, S.
- Potters, M.G.
- Ruffo, S.
DOIAbstract
We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and is normalized by a size-dependent constant. The exponent ? of the power law is taken in the range 0??<1. The oscillator frequency distribution is symmetric about its mean (taken to be zero) and is nonincreasing on [0,?). In the continuum limit, the local density of oscillators evolves in time following the continuity equation that expresses the conservation of the number of oscillators of each frequency under the dynamics. This equation admits as a stationary solution the unsynchronized state uniform both ...
Add to ORKG