Pinning synchronization of spatial diffusion coupled reaction-diffusion neural networks with and without multiple time-varying delays

Sampling-Based Event-Triggered Exponential Synchronization for Reaction-Diffusion Neural Networks

In this article, the exponential synchronization control issue of reaction-diffusion neural networks (RDNNs) is mainly resolved by the sampling-based event-triggered scheme under Dirichlet boundary conditions. Based on the sampled state information, the event-triggered control protocol is updated only when the triggering condition is met, which effectively reduces the communication burden and saves energy. In addition, the proposed control algorithm is combined with sampled-data control, which can effectively avoid the Zeno phenomenon. By thinking of the proper Lyapunov-Krasovskii functional and using some momentous inequalities, a sufficient condition is obtained for RDNNs to achieve exponential synchronization. Finally, some simulation results are shown to demonstrate the validity of the algorithm.

Global Exponential Synchronization of Coupled Delayed Memristive Neural Networks With Reaction-Diffusion Terms via Distributed Pinning Controls

This article presents new theoretical results on global exponential synchronization of nonlinear coupled delayed memristive neural networks with reaction-diffusion terms and Dirichlet boundary conditions. First, a state-dependent memristive neural network model is introduced in terms of coupled partial differential equations. Next, two control schemes are introduced: distributed state feedback pinning control and distributed impulsive pinning control. A salient feature of these two pinning control schemes is that only partial information on the neighbors of pinned nodes is needed. By utilizing the Lyapunov stability theorem and Divergence theorem, sufficient criteria are derived to ascertain the global exponential synchronization of coupled neural networks via the two pining control schemes. Finally, two illustrative examples are elaborated to substantiate the theoretical results and demonstrate the advantages and disadvantages of the two control schemes.

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.

Event-triggered passivity and synchronization of delayed multiple-weighted coupled reaction-diffusion neural networks with non-identical nodes

This paper solves the event-triggered passivity and synchronization problems for delayed multiple-weighted coupled reaction-diffusion neural networks (DMWCRDNNs) composed of non-identical nodes with and without parameter uncertainties. On one side, by designing appropriate event-triggered controllers, several passivity and synchronization criteria for DMWCRDNNs with certain parameters under the designed event-triggered conditions are derived based on the Lyapunov functional method and some inequality techniques. On the other side, we consider that the external perturbations may lead the parameters in network model to containing uncertainties, robust event-triggered passivity and synchronization for DMWCRDNNs with parameter uncertainties are investigated. Finally, two examples with numerical simulation results are provided to illustrate the effectiveness of the obtained theoretical results.

Passivity and Synchronization of Coupled Uncertain Reaction-Diffusion Neural Networks With Multiple Time Delays

This paper presents a complex network model consisting of N uncertain reaction-diffusion neural networks with multiple time delays. We analyze the passivity and synchronization of the proposed network model and derive several passivity and synchronization criteria based on some inequality techniques. In addition, by considering the difficulty in achieving passivity (synchronization) in such a network, an adaptive control scheme is also developed to ensure that the proposed network achieves passivity (synchronization). Finally, we design two numerical examples to verify the effectiveness of the derived passivity and synchronization criteria.