Fixed-time synchronization of stochastic memristor-based neural networks with adaptive control

In this study, we consider the fixed-time synchronization problem for stochastic memristor-based neural networks (MNNs) via two different controllers. First, a new stochastic differential equation is established using differential inclusions and set-valued maps. Next, two kinds of control protocols are designed, including a nonlinear delayed state feedback control scheme and a novel adaptive control strategy, by which fixed-time synchronization of MNNs can be achieved. Then based on stochastic analysis techniques and a Lyapunov function, some sufficient criteria are obtained to ensure that stochastic MNNs achieve stochastic fixed-time synchronization in probability. In addition, the upper bound of the settling time is estimated. Finally, simulation results are provided to demonstrate the validity of the proposed schemes.