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

Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials