Cluster synchronization for controlled nodes via the dynamics of edges in complex dynamical networks

• Published in: PloS one Vol. 18; no. 8; p. e0288657
• Main Authors: Liu, Lizhi, Chen, Cao, Gao, Zilin, Cheng, Bo
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 03-08-2023
• Subjects: Analysis; Behavior; Biology and Life Sciences; Clusters; Complex systems; Computer and Information Sciences; Control theory; Coupling; Design; Dynamical systems; Engineering and Technology; Evolution; Mathematical models; NOD-like receptors; Nodes; Physical Sciences; Research and Analysis Methods; Social Sciences; Structure-function relationships; Synchronism; Synchronization; China; Iran
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0288657

An appropriate dynamic coupling form between nodes and edges' state can effectively promote the emergence of desired network function (phenomenon), but the existing literatures have not conducted in-depth research on the coupling mechanism. This paper mainly focuses on the coupling auxiliary mechanism of dynamic edges for the emergence of cluster phenomenon of nodes, explores the essential relation between structure and function in complex dynamical networks (CDNs). Firstly, a novel model of CDNs has dynamic systems attached on not only nodes but also edges is proposed from the viewpoint of large-scale system. Secondly, a feedback nodes controller is synthesized associate with the designed linear and adaptive dynamics of edges. Via the appropriate dynamic behaviors of the edges system, the controlled nodes can realize cluster synchronized. Finally, the validity of the proposed approaches is verified by a given numerical example.