Laplacian Spectra and Coherence Analysis of Asymmetric Networks Under Noise Disturbance

Abstract In this paper, we propose a class of asymmetric networks with two different coupling styles to highlight the impact of network parameters and leader position on network coherence. Firstly, the exact analytical expressions for the leaderless coherence of two networks are derived. Secondly, we select several distinct schemes for assigning leaders to the networks and derive the corresponding expressions between leader-follower coherence and network parameters. Thirdly, the coherence and robustness properties of the networks are further analyzed based on the previously derived theoretical results. Finally, the Kirchhoff index, global mean first-passage time, and Laplacian energy of the networks are analyzed. Based on the analysis results of this paper, we can conclude that leader position and network parameters have a profound impact on coherence. Specifically, the coupled networks with no chain connections in the middle exhibit better coherence performance. The analytical results obtained above provide a new perspective and theoretical foundation for the optimal design of coordination mechanisms in distributed systems.