Synchronization of quaternion-valued multi-layer coupled networks: An adaptive activation-time-based event-triggered scheme

This paper develops an adaptive activation-time-based event-triggered scheme (ETS) to investigate the synchronization of quaternion-valued multi-layer coupled networks (QVMLCNs). Firstly, the QVMLCN models with linear coupling and nonlinear coupling are established, respectively. Subsequently, a new adaptive activation-time-based ETS that can only be activated after some particular moments is presented to address the synchronization issue of the considered two types of QVMLCNs. It is worth emphasizing that the principal advantage of the proposed adaptive activation-time-based ETS is that Zeno behavior can be naturally excluded and a positive minimum interevent time can be strictly ensured, which is more resource-conserving than existing adaptive ETSs. Lastly, the usefulness of the theoretical results is verified by some numerical simulations.