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Article

Secure Dynamic Event-Triggered Cluster Synchronization Control of Complex Dynamical Networks Under Random Deception Attacks

1
School of Economics and Statistics, Guangzhou University, Guangzhou 510000, China
2
School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510000, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(23), 3797; https://doi.org/10.3390/math13233797
Submission received: 14 October 2025 / Revised: 18 November 2025 / Accepted: 23 November 2025 / Published: 26 November 2025
(This article belongs to the Special Issue Dynamics on Complex Networks: Theory, Modelling, and Applications)

Abstract

This paper is concerned with the secure and resource-efficient cluster synchronization problem of a class of complex dynamical networks (CDNs) under random deception attacks. Each node in the CDNs is modeled by a nonlinear dynamical system with multiple time-varying delays and nonlinear couplings. The central aim is to make each cluster of nodes converge to the same reference trajectory that is distinct for each cluster regardless of the adverse effects of random deception attacks while ensuring communication efficiency for each node. Toward this aim, a distributed dynamic event-triggered mechanism is first proposed such that each node can make its own decisions to transmit or not its data of interest over the communication channel. Second, by suitably modeling the random deception attacks, secure and event-based cluster synchronization controllers are constructed, which incorporate both the effects of random deception attacks and intermittent data arrivals. Then, sufficient conditions ensuring the secure cluster synchronization of the delayed CDNs under randomly occurring deception attacks are established by constructing some appropriate Lyapunov functionals. Furthermore, tractable design criteria on the existence of desired cluster synchronization controllers are derived. Finally, an illustrative example is presented to validate the effectiveness of the main theoretical results.
Keywords: complex dynamical networks; cluster synchronization; deception attacks; dynamic event-triggered mechanism complex dynamical networks; cluster synchronization; deception attacks; dynamic event-triggered mechanism

Share and Cite

MDPI and ACS Style

Yu, Y.; Liu, L. Secure Dynamic Event-Triggered Cluster Synchronization Control of Complex Dynamical Networks Under Random Deception Attacks. Mathematics 2025, 13, 3797. https://doi.org/10.3390/math13233797

AMA Style

Yu Y, Liu L. Secure Dynamic Event-Triggered Cluster Synchronization Control of Complex Dynamical Networks Under Random Deception Attacks. Mathematics. 2025; 13(23):3797. https://doi.org/10.3390/math13233797

Chicago/Turabian Style

Yu, Yuncai, and Ling Liu. 2025. "Secure Dynamic Event-Triggered Cluster Synchronization Control of Complex Dynamical Networks Under Random Deception Attacks" Mathematics 13, no. 23: 3797. https://doi.org/10.3390/math13233797

APA Style

Yu, Y., & Liu, L. (2025). Secure Dynamic Event-Triggered Cluster Synchronization Control of Complex Dynamical Networks Under Random Deception Attacks. Mathematics, 13(23), 3797. https://doi.org/10.3390/math13233797

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