Volume 35_3-4_(2014)_189-206

Dephasing of Kuramoto oscillators in kinetic regime towards a fixed asymptotically free state
Benedetto D. - Caglioti, E. - Montemagno, U.

Abstract. We study the kinetic Kuramoto model for coupled oscillators. We prove that for any regular free state, if the interaction is small enough, it exists a solution which converges to it. For this class of solution the order parameter vanishes to zero, showing a behavior similar to the phenomenon of Landau damping in plasma physics. We obtain an exponential decay of the order parameter in the case on analytical regularity of the asymptotic state, and a polynomial decay in the case of Sobolev regularity.

Rend. Mat. Appl. (7) 35 (2014) 189-206;  pdf