  We analyze the emergence of wiggling temporal localized states in a passively
mode-locked Vertical External- Cavity Surface-Emitting Laser composed by a gain
chip and a resonant saturable absorber mirror. We show that the wiggling
instability stems from the interplay between the third-order dispersion induced
by the micro-cavities and their frequency mismatch. The latter is identified as
an experimentally crucial parameter defining the range of existence of stable
emission. We reveal the homoclinic scenario underlying the wiggling phenomenon
and we show how it allows to control the oscillation.
