Finite-time cluster synchronization of nonlinearly coupled reaction-diffusion neural networks via spatial coupling and control

The finite-time cluster synchronization (FTCS) problem of nonlinearly coupled (NC) reaction-diffusion neural networks (RDNNs) with hybrid coupling via control is investigated. The coupling matrix for the network can be asymmetric. We design a control strategy only depending on initial states of the network, which can not only help the network achieve the cluster synchronization, and even the FTCS. This can be regarded as the main contribution of this paper. Some criteria for FTCS are obtained from rigorous proof. Finally, we also present the results of numerical simulations.