Finite-Time Synchronization and H∞ Synchronization for Coupled Neural Networks With Multistate or Multiderivative Couplings.

This article investigates the finite-time synchronization (FTS) and H∞ synchronization for two types of coupled neural networks (CNNs), that is, the cases with multistate couplings and with multiderivative couplings. By designing appropriate state feedback controllers and parameter adjustment strategies, some FTS and finite-time H∞ synchronization criteria for CNNs with multistate couplings are derived. In addition, we further consider the FTS and finite-time H∞ synchronization problems for CNNs with multiderivative couplings by utilizing state feedback control approach and selecting suitable parameter adjustment schemes. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed criteria.

Analysis and Control of Output Synchronization in Directed and Undirected Complex Dynamical Networks.

This research focuses on the problem of output synchronization in undirected and directed complex dynamical networks, respectively, by applying Barbalat's lemma. First, to ensure the output synchronization, several sufficient criteria are established for these network models based on some mathematical techniques, such as the Lyapunov functional method and matrix theory. Furthermore, some adaptive schemes to adjust the coupling weights among network nodes are developed to achieve the output synchronization. By applying the designed adaptive laws, several criteria for output synchronization are deduced for the network models. In addition, a design procedure of the adaptive law is shown. Finally, two simulation examples are used to show the effectiveness of the previous results.

Passivity and Output Synchronization of Complex Dynamical Networks With Fixed and Adaptive Coupling Strength.

This paper considers a complex dynamical network model, in which the input and output vectors have different dimensions. We, respectively, investigate the passivity and the relationship between output strict passivity and output synchronization of the complex dynamical network with fixed and adaptive coupling strength. First, two new passivity definitions are proposed, which generalize some existing concepts of passivity. By constructing appropriate Lyapunov functional, some sufficient conditions ensuring the passivity, input strict passivity and output strict passivity are derived for the complex dynamical network with fixed coupling strength. In addition, we also reveal the relationship between output strict passivity and output synchronization of the complex dynamical network with fixed coupling strength. By employing the relationship between output strict passivity and output synchronization, a sufficient condition for output synchronization of the complex dynamical network with fixed coupling strength is established. Then, we extend these results to the case when the coupling strength is adaptively adjusted. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the proposed criteria.

Passivity of Directed and Undirected Complex Dynamical Networks With Adaptive Coupling Weights.

A complex dynamical network consisting of N identical neural networks with reaction-diffusion terms is considered in this paper. First, several passivity definitions for the systems with different dimensions of input and output are given. By utilizing some inequality techniques, several criteria are presented, ensuring the passivity of the complex dynamical network under the designed adaptive law. Then, we discuss the relationship between the synchronization and output strict passivity of the proposed network model. Furthermore, these results are extended to the case when the topological structure of the network is undirected. Finally, two examples with numerical simulations are provided to illustrate the correctness and effectiveness of the proposed results.

Pinning Control Strategies for Synchronization of Linearly Coupled Neural Networks With Reaction-Diffusion Terms.

Two types of coupled neural networks with reaction-diffusion terms are considered in this paper. In the first one, the nodes are coupled through their states. In the second one, the nodes are coupled through the spatial diffusion terms. For the former, utilizing Lyapunov functional method and pinning control technique, we obtain some sufficient conditions to guarantee that network can realize synchronization. In addition, considering that the theoretical coupling strength required for synchronization may be much larger than the needed value, we propose an adaptive strategy to adjust the coupling strength for achieving a suitable value. For the latter, we establish a criterion for synchronization using the designed pinning controllers. It is found that the coupled reaction-diffusion neural networks with state coupling under the given linear feedback pinning controllers can realize synchronization when the coupling strength is very large, which is contrary to the coupled reaction-diffusion neural networks with spatial diffusion coupling. Moreover, a general criterion for ensuring network synchronization is derived by pinning a small fraction of nodes with adaptive feedback controllers. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

Passivity and Synchronization of Linearly Coupled Reaction-Diffusion Neural Networks With Adaptive Coupling.

In this paper, we study a general array model of coupled reaction-diffusion neural networks (NNs) with adaptive coupling. In order to ensure the passivity of the coupled reaction-diffusion neural networks, some adaptive strategies to tune the coupling strengths among network nodes are designed. By utilizing some inequality techniques and the designed adaptive laws, several sufficient conditions ensuring passivity are obtained. In addition, we reveal the relationship between passivity and synchronization of the coupled reaction-diffusion NNs. Based on the obtained passivity results and the relationship between passivity and synchronization, a global synchronization criterion is established. Finally, numerical simulations are presented to illustrate the correctness and effectiveness of the proposed results.