Robustness of consensus in m-rose networks

Abstract

The consensus of deterministic networks investigates the relationships between consensus and network topology, which can be measured by network coherence. The m-rose networks are composed of m circles, which share a common node. Recently, scholars have obtained the first-order coherence of 5-rose networks. This paper takes the more general m-rose networks as the research object, firstly, the m-rose networks are introduced. Secondly, the relationships between Laplacian eigenvalues and polynomial coefficients are used to obtain the first-order and second-order coherence of the m-rose networks. Finally, the effects of topology parameters such as the number of petals m and the length of a cycle n on the robustness of network consensus are discussed, and the validity of the conclusion is verified by numerical simulation.