Event-Based Global Exponential Synchronization for Quaternion-Valued Fuzzy Memristor Neural Networks With Time-Varying Delays

As quaternion-valued memristor neural networks (MNNs) have important applications in many engineering fields and the information in the real world is often uncertain and inaccurate, therefore, in order to better apply to practice, it is necessary to study the dynamic behaviors of quaternion-valued MNNs with fuzzy logic. In this article, the event-based synchronization problem for quaternion-valued Takagi-Sugeno (T-S) fuzzy MNNs (QVT-SFMNNs) with time-varying delays is studied. Different from the existing synchronization results of MNNs, T-S fuzzy logic and quaternion are simultaneously considered in the MNNs, which makes the model more applicable. Based on some algebraic properties of quaternions, a novel event-based fuzzy controller and some static and dynamic event trigger conditions are designed. By constructing simple Lyapunov functions instead of complex Lyapunov functionals and using Halanay inequality, several sufficient criteria are given to ensure the global exponential synchronization between the considered QVT-SFMNNs. Meanwhile, the Zeno behaviors of the response QVT-SFMNN under different event trigger conditions are excluded. It is important to note that the results obtained in article are less conservative and applicable to low-dimensional complex-valued and real-valued MNNs. Finally, a numerical example is given to verify the validity of the obtained theoretical results.