Synchronization and stability of delayed fractional-order memristive quaternion-valued neural networks with parameter uncertainties

Abstract

This paper investigates the synchronization and stability problem of fractional-order memristive quaternion-valued neural networks (FMQVNNs) with time delay and uncertain parameters. Due to the quaternion multiplication’s non-commutativity resulting from Hamilton rules, the studied FMQVNNs are converted into the relevant four memristive real-valued neural networks (MRVNNs). Consequently, the synchronization and stability problem of FMQVNNs can be analyzed by studying the corresponding ones of the four MRVNNs. Mainly based on nonsmooth analysis, Lyapunov direct method and comparison theory, some proper criteria are established to ensure the global asymptotical synchronization and stability for the given systems. Finally, a numerical example is shown to demonstrate the effectiveness of the theoretical results.