Phase-mixing v.s. phase synchronization in the dynamics of flow-shear induced edge transport barrier

Nonlinear relaxation oscillations of flow-shear induced transport barriers can be qualitatively reproduced using a phenomenological critical-gradient model [M. Leconte, Y.M. Jeon and G.S. Yun, \emph{Contrib. Plasma Phys.} 56, 736 (2016]. Here, we give a more in-depth analysis of the mechanism of these nonlinear oscillations, associated to nonlinear \emph{phase synchronization}, in an extended version of the model including random fluctuations.