Adaptive anti-synchronization and H∞ anti-synchronization for memristive neural networks with mixed time delays and reaction–diffusion terms

Finite-time synchronization of reaction-diffusion memristive neural networks: A gain-scheduled integral sliding mode control scheme

The finite-time synchronization issue of reaction-diffusion memristive neural networks (RDMNNs) is studied in this paper. To better synchronize the parameter-varying drive and response systems, an innovative gain-scheduled integral sliding mode control scheme is proposed, where the 2ⁿ controller gains can be scheduled and an integral switching surface function that contains a discontinuous term is involved. Moreover, by constructing a novel Lyapunov-Krasovskii functional and combining reciprocally convex combination (RCC) method, a less conservative finite-time synchronization criterion for RDMNNs is derived in the form of linear matrix inequalities (LMIs). Finally, three numerical simulations are exploited to illustrate the effectiveness, superiority and practicability of this paper.

Gain-Scheduled Finite-Time Synchronization for Reaction-Diffusion Memristive Neural Networks Subject to Inconsistent Markov Chains

An innovative class of drive-response systems that are composed of Markovian reaction-diffusion memristive neural networks, where the drive and response systems follow inconsistent Markov chains, is proposed in this article. For this kind of nonlinear parameter-varying systems, a suitable gain-scheduled controller that involves a mode and memristor-dependent item is designed, so that the error system is bounded within a finite-time interval. Moreover, by constructing a novel Lyapunov-Krasovskii functional and employing the canonical Bessel-Legendre inequality and free-weighting matrix method, the conservatism of the finite-time synchronization criterion can be greatly reduced. Finally, two numerical examples are provided to illustrate the feasibility and practicability of the obtained results.

Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.

Global Stabilization of Fuzzy Memristor-Based Reaction-Diffusion Neural Networks

This article investigates the global stabilization problem of Takagi-Sugeno fuzzy memristor-based neural networks with reaction-diffusion terms and distributed time-varying delays. By using the Green formula and proposing fuzzy feedback controllers, several algebraic criteria dependent on the diffusion coefficients are established to guarantee the global exponential stability of the addressed networks. Moreover, a simpler stability criterion is obtained by designing an adaptive fuzzy controller. The results derived in this article are generalized and include some existing ones as special cases. Finally, the validity of the theoretical results is verified by two examples.

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks.

Exponential Stability of Periodic Solution for Impulsive Memristor-Based Cohen–Grossberg Neural Networks with Mixed Delays

Memristor, as the future of artificial intelligence, has been widely used in pattern recognition or signal processing from sensor arrays. Memristor-based recurrent neural network (MRNN) is an ideal model to mimic the functionalities of the human brain due to the physical properties of memristor. In this paper, the periodicity for memristor-based Cohen–Grossberg neural networks (MCGNNs) is studied. The neural network (NN) considered in this paper is based on the memristor and involves time-varying delays, distributed delays and impulsive effects. The boundedness and monotonicity of the activation function are not assumed. By some inequality technique and contraction mapping principle, we prove the existence, uniqueness and exponential stability of periodic solution for MCGNNs. Finally, some numeral examples and comparisons are provided to illustrate the validation of our results.

Exponential synchronization of generalized neural networks with mixed time-varying delays and reaction-diffusion terms via aperiodically intermittent control

In this paper, the exponential synchronization problem of generalized reaction-diffusion neural networks with mixed time-varying delays is investigated concerning Dirichlet boundary conditions in terms of p-norm. Under the framework of the Lyapunov stability method, stochastic theory, and mathematical analysis, some novel synchronization criteria are derived, and an aperiodically intermittent control strategy is proposed simultaneously. Moreover, the effects of diffusion coefficients, diffusion space, and stochastic perturbations on the synchronization process are explicitly expressed under the obtained conditions. Finally, some numerical simulations are performed to illustrate the feasibility of the proposed control strategy and show different synchronization dynamics under a periodically/aperiodically intermittent control.