This article focuses on achieving fixed-time synchronization (FxTS) of nonlinear coupled memristive neural networks (NCMMN) with time delays. We propose a novel integrable sliding-mode manifold (SMM) and develop two control strategies (chattering or non-chattering) to achieve FxTS. By selecting appropriate parameters, some criteria are established to force the dynamics of NCMMN to reach the designed SMM within a fixed time and remain on it thereafter. Additionally, they provide estimations for the settling time (TST). the validity of our results is demonstrated through several numerical examples.

The mean square synchronization for a class of general stochastic delayed neural networks is explored in this paper using pinning impulsive control (PIC). It is evident that PIC combines the profits of pinning control and impulsive control. Considering that there is a time delay between the allocation and execution of impulsive instructions in practice, the idea of average impulsive delay (AID) is brought to describe this kind of delay. Furthermore, in actuality, neural networks with internal delay and stochastic disturbance are more general. Accordingly, some appropriate criteria are derived using the Lyapunov stability theory and the Fubini theorem to ensure mean square synchronization in two different cases, namely when the controller is designed with and without the impulsive delay. Finally, some numerical examples are afforded to validate the efficiency of theoretical results.