  A multiplex network of identical dynamical units becomes resilient against
parameter perturbation by adding selective linear diffusive cross-coupling
links. A parameter drift at any instant in one or multiple network nodes can
destroy synchrony, causing failure and even collapse in the network
performance. We introduced [PRE 95, 062204(2017)] a recovery strategy by
selective addition of cross-coupling links to save synchrony in the network
from the edge of failure due to parameter mismatch (small or large) in any
nodes. This concept is extended to 2-layered multiplex networks when the
emergent synchrony becomes resilient against a small or large parameter
drifting. In addition, the stability of the synchronous state is enhanced from
local stability to global stability of synchrony. By the addition of
cross-coupling, the network revives complete synchrony in all the nodes except
the perturbed nodes, which emerges into a type of generalized synchrony with
all the unperturbed nodes. The generalized synchrony is manifested simply by a
linear amplitude response in the state variable(s) of the perturbed node(s) by
a scaling factor proportional to the mismatch. A set of systematic rules has
been derived from the linear flow matrix of the dynamical system representing
the nodes dynamics that helps find the connectivity matrix of the
cross-coupling links. Lyapunov function stability condition is used to
determine the cross-coupling link strength that, in turn, establishes global
stability of synchrony of the multiplex network. We verify the efficacy of our
proposed coupling scheme with analytical results and numerical simulations of
two examples of multiplex networks. In the first example, we use non-local
connectivity in each layer, with nodal dynamics of the FitzHugh-Nagumo neuron
model.
