Exponential synchronization of stochastic time-delayed memristor-based neural networks via distributed impulsive control

Robust exponential stability of discrete-time uncertain impulsive stochastic neural networks with delayed impulses

This paper is devoted to the study of the robust exponential stability (RES) of discrete-time uncertain impulsive stochastic neural networks (DTUISNNs) with delayed impulses. Using Lyapunov function methods and Razumikhin techniques, a number of sufficient conditions for mean square (RES-ms) robust exponential stability are derived. The obtained results show that the hybrid dynamic is RES-ms with regard to lower boundary of impulse interval if the discrete-time stochastic neural networks (DTSNNs) is RES-ms and that the impulsive effects are instable. Conversely, if DTSNNs is not RES-ms, impulsive effects can induce unstable neural networks (NNs) to stabilize again concerning an upper bound of the impulsive interval. The results obtained in this study have a broader scope of application than some previously existing findings. Two numerical examples were presented to verify the availability and advantages of the results.

The Synchronization Analysis of Cohen-Grossberg Stochastic Neural Networks with Inertial Terms

The exponential synchronization (ES) of Cohen-Grossberg stochastic neural networks with inertial terms (CGSNNIs) is studied in this paper. It is investigated in two ways. The first way is using variable substitution to transform the system to another one and then based on the properties of i t ^ o integral, differential operator, and the second Lyapunov method to get a sufficient condition of ES. The second way is based on the second-order differential equation, the properties of calculus are used to get a sufficient condition of ES. At last, results of the theoretical derivation are verified by virtue of two numerical simulation examples.

Dynamical and static multisynchronization analysis for coupled multistable memristive neural networks with hybrid control

This paper investigates the dynamical multisynchronization (DMS) and static multisynchronization (SMS) problems for a class of delayed coupled multistable memristive neural networks (DCMMNNs) via a novel hybrid controller which includes delayed impulsive control and state feedback control. Based on the state-space partition method and the geometrical properties of the activation function, each subnetwork has multiple locally exponential stable equilibrium states. By employing a new Halanay-type inequality and the impulsive control theory, some new linear matrix inequalities (LMIs)-based sufficient conditions are proposed. It is shown that the delayed impulsive control with suitable impulsive interval and allowable time-varying delay can still guarantee the DMS and SMS of DCMMNNs. Finally, a numerical example is presented to illustrate the effectiveness of the hybrid controller.

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.