Pinning synchronization of multiple fractional-order fuzzy complex-valued delayed spatiotemporal neural networks

The implications of neural synchronization extend beyond brain function, and can impact the development of artificial neural networks. This paper explores the synchronization of multiple fractional-order fuzzy complex-valued spatiotemporal neural networks (MFOFCVSNNs), which is novel and characterized using fuzzy logic and fractional-order partial differential equations, making it more adaptable and versatile. We first establish a new fractional-order complex-valued partial differential inequality, an integer-order complex-valued partial differential inequality, and an equation. Then, by combining the Lyapunov method with fuzzy set theory, employing newly established inequalities and equations, along with a newly designed fuzzy pinning controller, we derive two linear matrix inequality (LMI) formulations of synchronization criteria for MFOFCVSNNs using a direct non-complex decomposition approach. These criteria exhibit different dependencies on the membership function, with one being independent and the other dependent. Importantly, the criterion based on the membership function demonstrates reduced conservatism compared to its independent counterpart. By leveraging M-matrix theory, we present the synchronization criteria in a concise low-dimensional form. Moreover, this paper extends and enhances previous findings, resulting in reduced conservatism. Finally, we validate our theoretical analysis through numerical simulations.