  This paper is devoted to the generalized differential study of the normal
cone mappings associated with a large class of parametric constraint systems
(PCS) that appear, in particular, in nonpolyhedral conic programming.
Conducting a local second-order analysis of such systems, we focus on computing
the (primal-dual) graphical derivative of the normal cone mapping under the
$C^2$-cone reducibility of the constraint set together with the fairly weak
metric subregularity constraint qualification and its uniform parametric
counterpart known as Robinson stability. The obtained precise formulas for
computing the underlying second-order object are applied to the derivation of
comprehensive conditions ensuring the important stability property of isolated
calmness for solution maps to parametric variational systems associated with
the given PCS.
