Generic evolutionarily stable strategies are DSC-stable

An evolutionary equilibrium is DSC-stable if it is (a) Dynamically stable, i.e., if the system at equilibrium is slightly disturbed, it returns to it, (b) Structurally stable, i.e., preserves defining properties for small perturbations of the underlying structure of the system, (c) Conceptually stable, i.e., equivalent to at least one other evolutionary equilibrium (concept), for a non-singleton class of dynamics.
Attractiveness is a minor refinement of the defining properties of certain evolutionary equilibria. We show that attractive evolutionarily stable strategies, attractive evolutionarily stable equilibria and attractive truly evolutionarily stable states are DSC-stable for specific (`dense') classes of dynamics, and that each strict saturated (Nash) equilibrium is DSC-stable for a vast class of evolutionary dynamics.
So, generically neither the exact specification of the dynamic system, nor the equilibrium concept matter for qualitative conclusions about the system's behavior nearby.