Cluster synchronization for a class of complex dynamical network system with randomly occurring coupling delays via an improved event-triggered pinning control approach

• Published in: Journal of the Franklin Institute Vol. 357; no. 4; pp. 2167 - 2184
• Main Authors: Lu, Hongqian, Hu, Yue, Guo, Chaoqun, Zhou, Wuneng
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01-03-2020; Elsevier Science Ltd
• Subjects: Clusters; Computer simulation; Controllers; Coupling; Dynamical systems; Nodes; Pinning; Simulation; Stability criteria; Synchronism
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2019.11.076

This paper discusses the cluster synchronization problem for a class of complex dynamical networks with coupling time delays. Under the randomly occurring coupling time delays condition, a novel complex network model is established to express the dynamical behavior of the nodes more precisely. An improved event-triggered mechanism is proposed for two purpose containing the reduction of network burden and improvement of cluster synchronization efficiency. The pinning control strategy is adopted for cluster synchronization via controlling a small fraction of the network nodes. By employing Lyapunov–Krasovskii functional method, a stability criterion is obtained to ensure the achievement of cluster synchronization and a event-triggered pinning controller is constructed. Finally, a simulation example is expressed to verify the effectiveness of our main results.