  We consider the coupling between two networks, each having N nodes whose
individual dynamics is modeled by a two-state master equation. The
intra-network interactions are all to all, whereas the inter-network
interactions involve only a small percentage of the total number of nodes. We
demonstrate that the dynamics of the mean field for a single network has an
equivalent description in terms of a Langevin equation for a particle in a
double-well potential. The coupling of two networks or equivalent coupling of
two Langevin equations demonstrates synchronization or antisynchronization
between two systems, depending on the sign of the interaction. The
anti-synchronized behavior is explained in terms of the potential function and
the inter-network interaction. The relative entropy is used to establish that
the conditions for maximum information transfer between the networks are
consistent with the Principle of Complexity Management and occurs when one
system is near the critical state. The limitations of the Langevin modeling of
the network coupling are also discussed.
