Synchronization for multiweighted and directly coupled reaction-diffusion neural networks with hybrid coupling via boundary control

This paper deals with the synchronization issue of multiweighted and directed coupled reaction-diffusion neural networks with hybrid coupling (MDCRDNNHC) based on boundary control. Spatial information is used for synchronization accompanied by state information, which is called hybrid coupling. By constructing appropriate controllers located in the boundary, synchronization matter for MDCRDNNHC with nonzero boundary values is solved. Inner coupling matrices (IMs) and outer coupling matrices (OMs) can be directed, competitive and even not connected in this paper. We propose a novel strategy to fuse current two technical routes for directed networks with multiweights. For MDCRDNNHC with diagonal IMs, we prove that if the weighted (added) combinations of multiple OMs for each dimension are strongly connected, and the Chebyshev distance among their normalized left eigenvectors of added OMs corresponding to zero eigenvalue for each dimension is less than a threshold, then synchronization can be attained. In addition, it is also applicable for positive definite but non-diagonal IMs under this fusion technique. Numerical examples are finally provided to demonstrate the effectiveness of these theoretical results.