Interlayer impacts to deep-coupling dynamical networks: A snapshot of equilibrium stability.

This paper defines deep-coupling networks with two categories of interlayer structures and investigates the equilibrium stability, when every node in the network is governed by a differential dynamical system. Several stability criteria of the equilibrium of deep-coupling networks are arrived at when the equilibrium of each node system is stable or unstable in two categories of interlayer couplings, which clarify interlayer impacts with the dependence of network topology and intralayer intensity as well. Several two-layer and three-layer numerical examples are provided to verify the analytical results.