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.