IOD-type continuity-sets of bi-spatial attractors for random nonautonomous FitzHugh-Nagumo equations

We discuss the continuity-set for a family of pullback random bi-spatial attractors, with respect to the Hausdorff metric on the end space. Under six conditions, we show that the continuity-set is an IOD-type (Intersection of countably many Open Dense sets) in the index space and has the continuum cardinality, which extend the recent results from the initial space to the end space. Applying the abstract results to random nonautonomous FitzHugh-Nagumo equations driven by a family of Wong-Zakai processes with a noise-size in (0, ∞], where the infinity corresponds to the deterministic equation, we prove the existence and IOD-type continuity of pullback random bi-spatial attractors in the higher order Lebesgue space with respect to the noise-size, moreover, the continuity-set is dense with the continuum cardinality.