Robustness of consensus in double‐layer degree positive and negative correlation ring networks

Abstract

The robustness of consensus in multilayer networks is affected by the network structure, especially the interlayer coupling approach. The article investigates the impact of two interlayer coupling approaches on the robustness of consensus in double‐layer ring networks, where the interlayer relationships are denoted as degree positive correlation (PC) and degree negative correlation (NC), respectively. The robustness of network consensus can be derived from network coherence. Two types of network coherence are first described using the Kirchhoff index and the number of spanning trees, providing a new calculation method for network coherence. The number of network nodes and the coupling strength have been shown to impact the coherence of the two types of networks. Combined with numerical simulation experiments, the NC model shows better consensus than the PC model under the same parameter set. In particular, the parameter values when the network consensus is optimal are obtained.