Passivity Analysis for Quaternion-Valued Memristor-Based Neural Networks With Time-Varying Delay

Dynamic Event-Triggered Control for GSES of Memristive Neural Networks Under Multiple Cyber-Attacks

In this article, the dynamic event-triggered control problem of memristive neural networks (MNNs) under multiple cyber-attacks is considered. A novel dynamic event-triggering scheme (DETS) and the corresponding event-triggered controller are proposed by taking into consideration both denial-of-service and deception attacks (DoS-DAs). Then, a key lemma is established to show that the dynamic event-triggered controller can be used to solve the globally stochastically exponential stability (GSES) issue of concerned MNN under multiple cyber-attacks. Meanwhile, a novel Lyapunov functional is proposed based on the actual sampling pattern. It is shown that under our proposed dynamic event-triggered controller and Lyapunov functional, the concerned MNN can achieve GSES in the presence of DoS-DAs. In addition, our results include relevant results on event-triggered control of MNN with static event-triggering scheme (SETS) or without cyber-attacks as special cases. The effectiveness of the proposed event-triggered controller under multiple cyber-attacks is illustrated by a simulation example.

Finite-time passivity of neutral-type complex-valued neural networks with time-varying delays

In this work, we investigated the finite-time passivity problem of neutral-type complex-valued neural networks with time-varying delays. On the basis of the Lyapunov functional, Wirtinger-type inequality technique, and linear matrix inequalities (LMIs) approach, new sufficient conditions were derived to ensure the finite-time boundedness (FTB) and finite-time passivity (FTP) of the concerned network model. At last, two numerical examples with simulations were presented to demonstrate the validity of our criteria.

Fixed-Time Pinning Common Synchronization and Adaptive Synchronization for Delayed Quaternion-Valued Neural Networks

This article focuses on the fixed-time pinning common synchronization and adaptive synchronization for quaternion-valued neural networks with time-varying delays. First, to reduce transmission burdens and limit convergence time, a pinning controller which only controls partial nodes directly rather than the entire nodes is proposed based on fixed-time control theory. Then, by Lyapunov function approach and some inequalities techniques, fixed-time common synchronization criterion is established. Second, further to realize the self-regulation function of pinning controller, an adaptive pinning controller which can adjust automatically the control gains is developed, the desired fixed-time adaptive synchronization is achieved for the considered system, and the corresponding criterion is also derived. Finally, the availability of these results is tested by simulation example.

Proportional-Integral State Estimator for Quaternion-Valued Neural Networks With Time-Varying Delays

This brief investigates the problem of state estimation of quaternion-valued neural networks (QVNNs) with time-varying delays. First, by extending the Jensen inequality to quaternion domain, an extended Jensen inequality with quaternion term is derived. Second, a class of proportional-integral state estimator (PISE) with exponential decay term is proposed. Then, by constructing a suitable Lyapunov-Krasovskii functional (LKF), some sufficient conditions are obtained to ensure the existence of the designed PISE and the gain matrices of the designed PISE can be directly computed. Simulations are given to illustrate the advantage of the proposed method.

Finite-Time and Fixed-Time Synchronization of Quaternion-Valued Neural Networks With/Without Mixed Delays: An Improved One-Norm Method

In this article, the finite-time synchronization (FTSYN) of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed time delays is studied. Furthermore, the FTSYN and fixed-time synchronization (FIXSYN) of the QVNNs without time delay are investigated. Different from the existing results, which used decomposition techniques, by introducing an improved one-norm, we use a direct analytical method to study the synchronization problems. Incidentally, several properties of one-norm of the quaternion are analyzed, and then, three effective controllers are proposed to synchronize the drive and response QVNNs within a finite time or fixed time. Moreover, efficient criteria are proposed to guarantee that the synchronization of QVNNs with or without mixed time delays can be realized within a finite and fixed time interval, respectively. In addition, the settling times are reckoned. Compared with the existing work, our advantages are mainly reflected in the simpler Lyapunov analytical process and more general activation function. Finally, the validity and practicability of the conclusions are illustrated via four numerical examples.

Unified Analysis on the Global Dissipativity and Stability of Fractional-Order Multidimension-Valued Memristive Neural Networks With Time Delay

The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. The derived criteria have many advantages in a smaller calculation, lower conservatism, more diversity, and higher flexibility. Finally, we provide two numerical examples to express the availability and improvements of the theoretical results.

Multi-periodicity of switched neural networks with time delays and periodic external inputs under stochastic disturbances

This paper presents new theoretical results on the multi-periodicity of recurrent neural networks with time delays evoked by periodic inputs under stochastic disturbances and state-dependent switching. Based on the geometric properties of activation function and switching threshold, the neuronal state space is partitioned into 5ⁿ regions in which 3ⁿ ones are shown to be positively invariant with probability one. Furthermore, by using Itô's formula, Lyapunov functional method, and the contraction mapping theorem, two criteria are proposed to ascertain the existence and mean-square exponential stability of a periodic orbit in every positive invariant set. As a result, the number of mean-square exponentially stable periodic orbits increases to 3ⁿ from 2ⁿ in a neural network without switching. Two illustrative examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.