  In this work we characterize the dynamical instabilities of localized
structures exhibited by a recently introduced Gelens et al., Phys. Rev. A 75,
063812 2007 generalization of the Lugiato-Lefever model that includes a weakly
nonlocal response of an intracavity metamaterial. A rich scenario, in which the
localized structures exhibit different types of oscillatory instabilities,
tristability, and excitability, including a regime of conditional excitability
in which the system is bistable, is presented and discussed. Finally, it is
shown that the scenario is organized by a pair of Takens-Bogdanov codimension-2
points.
