Sliding mode control-based fixed-time stabilization and synchronization of inertial neural networks with time-varying delays

A novel fixed-time stability lemma and its application in the stability analysis of BAM neural networks

In this paper, we put forward an interesting fixed-time (FXT) stability lemma, which is based on a whole new judging condition, and the minimum upper bound for the stability start time is obtained. In the new FXT stability lemma, the mathematical relation between the upper bound of the stability start time and the system parameters is very simple, and the judgment condition only involves two system parameters. To indicate the usability of the new FXT stability lemma, we utilize it to study the FXT stability of a bidirectional associative memory neural network (BAMNN) with bounded perturbations via sliding mode control. To match the developed FXT stability lemma, novel sliding mode state variables and a two-layer sliding mode controller are designed. According to the developed FXT stability lemma, the perturbed BAMNN can achieve FXT stability under the devised sliding mode controller. The upper bound of the stability start time can be calculated easily by virtue of the control parameters, and the sufficient conditions guaranteeing that the perturbed BAMNN can achieve FXT stability have also been derived. Last, we provide some confirmatory simulations.

Resilient fixed-time stabilization of switched neural networks subjected to impulsive deception attacks

This article focuses on the resilient fixed-time stabilization of switched neural networks (SNNs) under impulsive deception attacks. A novel theorem for the fixed-time stability of impulsive systems is established by virtue of the comparison principle. Existing fixed-time stability theorems for impulsive systems assume that the impulsive strength is not greater than 1, while the proposed theorem removes this assumption. SNNs subjected to impulsive deception attacks are modeled as impulsive systems. Some sufficient criteria are derived to ensure the stabilization of SNNs in fixed time. The estimation of the upper bound for the settling time is also given. The influence of impulsive attacks on the convergence time is discussed. A numerical example and an application to Chua's circuit system are given to demonstrate the effectiveness of the theoretical results.

New exploration on bifurcation for fractional-order quaternion-valued neural networks involving leakage delays

During the past decades, many works on Hopf bifurcation of fractional-order neural networks are mainly concerned with real-valued and complex-valued cases. However, few publications involve the quaternion-valued neural networks which is a generalization of real-valued and complex-valued neural networks. In this present study, we explorate the Hopf bifurcation problem for fractional-order quaternion-valued neural networks involving leakage delays. Taking advantage of the Hamilton rule of quaternion algebra, we decompose the addressed fractional-order quaternion-valued delayed neural networks into the equivalent eight real valued networks. Then the delay-inspired bifurcation condition of the eight real valued networks are derived by making use of the stability criterion and bifurcation theory of fractional-order differential dynamical systems. The impact of leakage delay on the bifurcation behavior of the involved fractional-order quaternion-valued delayed neural networks has been revealed. Software simulations are implemented to support the effectiveness of the derived fruits of this study. The research supplements the work of Huang et al. (Neural Netw 117:67-93, 2019).

Fixed-time synchronization of discontinuous competitive neural networks with time-varying delays

In this article, the fixed-time (FXT) synchronization of discontinuous competitive neural networks (CNNs) involving time-varying delays is investigated. Firstly, two kinds of discontinuous FXT control schemes are proposed and two forms of Lyapunov function are constructed based on p-norm and 1-norm to discuss the FXT synchronization of CNNs. By means of nonsmooth analysis and some inequality techniques, some simple criteria are obtained to achieve FXT synchronization and the upper bound of the settling time with less conservativeness is provided. Furthermore, the effect of time scale on FXT synchronization of CNNs is considered. Lastly, some numerical results for an example are provided to demonstrate the derived theoretical results.