  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.
