Synchronization and Adaptive Control of an Array of Linearly Coupled Reaction-Diffusion Neural Networks With Hybrid Coupling

In this paper, we propose a general array model of coupled reaction-diffusion neural networks with hybrid coupling, which is composed of spatial diffusion coupling and state coupling. By utilizing the Lyapunov functional method combined with the inequality techniques, a sufficient condition is given to ensure that the proposed network model is synchronized. In addition, when the external disturbances appear in the network, a criterion is obtained to guarantee the H
_∞
synchronization of the network. Moreover, some adaptive strategies to tune the coupling strengths among network nodes are designed for reaching synchronization and H
_∞
synchronization. Some criteria for synchronization and H
_∞
synchronization are derived by using the designed adaptive laws. Numerical simulations are presented finally to demonstrate the effectiveness of the obtained theoretical results.