  Coupling cyber and physical systems gives rise to numerous engineering
challenges and opportunities. An important challenge is the contagion of
failure from one system to another, that can lead to large scale cascading
failures. On the other hand, self-healing ability emerges as a valuable
opportunity where the overlay cyber network can cure failures in the underlying
physical network. To capture both self-healing and contagion, we introduce a
factor graph representation of inter-dependent cyber-physical systems in which
factor nodes represent various node functionalities and the edges capture the
interactions between the nodes. We develop a message passing algorithm to study
the dynamics of failure propagation and healing in this representation. Through
applying a fixed-point analysis to this algorithm, we investigate the network
reaction to initial disruptions. Our analysis provides simple yet critical
guidelines for choosing network parameters to achieve resiliency against
cascading failures.
