Phase transition of RN-ERN coupled network in failure recovery process

We simulate the failure recovery process and study the phase transition from high network activity (HNA) state to low network activity (LNA) state of the coupled network consisting of a regular network (RN) and an Erdos-Rényi network (ERN). Two recovery mechanisms are considered, the internal recovery and the external recovery, in the failure recovery process. We find that the evolution of the coupled network is crucially dependent on the coupling strength c between the two subnetworks and the external recovery possibility r since RN is sensitive to external recovery. A weak coupling can drive coevolution of the subnetworks when r ≈ 1.0, while the synchronous HNA-LNA phase transition needs stronger coupling to occur when r is smaller. The internal recovery enhances the robustness of network which makes coevolution more difficult to take place.