On synchronization criterion for coupled discrete-time neural networks with interval time-varying delays

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.

Robust synchronization of an array of neural networks with hybrid coupling and mixed time delays

This paper is concerned with the global exponential synchronization for an array of hybrid coupled neural networks with leakage delay, time-varying discrete and distributed delays. By employing a novel augmented Lyapunov-Krasovskii functional (LKF), applying the theory of Kronecker product of matrices, Barbalat׳s Lemma and the technique of linear matrix inequality (LMI), delay-dependent sufficient conditions are obtained for the global exponential synchronization of the system. As an extension, robust synchronization criteria are derived for the corresponding system with parameter uncertainties. Some examples are given to show the effectiveness of the obtained theoretical results.

Synchronization criteria of discrete-time complex networks with time-varying delays and parameter uncertainties

This paper is pertained with the synchronization problem for an array of coupled discrete-time complex networks with the presence of both time-varying delays and parameter uncertainties. The time-varying delays are considered both in the network couplings and dynamical nodes. By constructing suitable Lyapunov-Krasovskii functional and utilizing convex reciprocal lemma, new synchronization criteria for the complex networks are established in terms of linear matrix inequalities. Delay-partitioning technique is employed to incur less conservative results. All the results presented here not only depend upon lower and upper bounds of the time-delay, but also the number of delay partitions. Numerical simulations are rendered to exemplify the effectiveness and applicability of the proposed results.