Synchronization and control for directly coupled reaction-diffusion neural networks with multiweights and hybrid coupling

This paper mainly deals with the synchronization and pinning control for multiweighted, directly, and hybridly coupled reaction-diffusion neural networks (MDHCRDNNs). Different communication channels are expressed by multiple coupling matrices, while hybrid coupling means that state information combined with spatial diffusion information are employed jointly to attain synchronization. In comparison to previously published literature on multiweighted networks, outer matrices (OMs) in our paper can be directly coupled, with negative elements, and not even connected. One novel synchronization strategy is proposed to address directed networks with multiweights by integrating state matrices and spatial matrices into new union matrices. Then, for MDHCRDNNs, we obtain if the weighted groups of added OMs for each dimension are strongly connected, then synchronization and pinning synchronization criteria are derived. Furthermore, synchronization for adaptive coupling strength is solved as well. Finally, the effectiveness of these obtained results is verified through simulation examples.