Cluster Secure Synchronization of Complex Networks With Cooperative-Competitive Interaction Under DoS Attacks

作者：Ning Li, Dongyu He, Jianwei Shen, Zhiguo Shi · 发表于：IEEE Transactions on Network Science and Engineering · 年份：2025 · DOI：10.1109/tnse.2025.3628850 · 被引用次数：2 · 研究领域：Neural Networks Stability and Synchronization、Cooperative Communication and Network Coding、Distributed Control Multi-Agent Systems

This study investigates the cluster secure synchronization problem in cooperative-competitive networks subject to Denial-of-Service (DoS) attacks. First, a mathematical model of the cooperative-competitive networks with a weak competition coupling is proposed, where interactions between network nodes are represented by a signed graph that may be either structurally balanced or unbalanced. The network nodes are partitioned into$q$distinct clusters, with each node within a cluster exhibiting unique self-dynamics. Next, a cluster synchronization error system is formulated under the condition of DoS attacks when the pinning control scheme is utilized. By designing a suitable Lyapunov candidate function and applying advanced inequality techniques, cluster secure synchronization criteria for cooperative-competitive networks are derived. Synchronization analysis reveal that increasing intracluster coupling strength can significantly enhance the network's robustness against DoS attacks. Finally, two optimization algorithms are proposed to obtain the minimum allowable coupling strength and maximum allowable DoS attack rate, respectively, and the effectiveness of the proposed cluster synchronization condition is validated through two representative examples.