AUTHOR=Du Weiwei , Zhu Jian , Gao Haiping , Li Xianyong 

TITLE=Robustness of consensus in m-rose networks

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1199180

DOI=10.3389/fphy.2023.1199180

ISSN=2296-424X

ABSTRACT=<p>The consensus of deterministic networks investigates the relationships between consensus and network topology, which can be measured by network coherence. The <italic>m</italic>-rose networks are composed of <italic>m</italic> circles, which share a common node. Recently, scholars have obtained the first-order coherence of 5-rose networks. This paper takes the more general <italic>m</italic>-rose networks as the research object, firstly, the <italic>m</italic>-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 <italic>m</italic>-rose networks. Finally, the effects of topology parameters such as the number of petals <italic>m</italic> and the length of a cycle <italic>n</italic> on the robustness of network consensus are discussed, and the validity of the conclusion is verified by numerical simulation.</p>