Lag Synchronization and Lag $\mathcal {H}_{\infty }$ Synchronization for Multiweighted Coupled Reaction–Diffusion Neural Networks Suffering Topology Attacks

This paper mainly discusses two kinds of coupled reaction-diffusion neural networks (CRNN) under topology attacks, that is, the cases with multistate couplings and with multiple spatial-diffusion couplings. On one hand, by adopting state feedback control scheme, the problem of the lag synchronization for the multistate coupled CRNN is addressed. Moreover, the influences of external disturbances for the lag synchronization of the CRNN with multistate couplings are also taken into consideration. On the other hand, several lag and lag $\mathcal {H}_{\infty }$ synchronization conditions for CRNN with multiple spatial-diffusion couplings are derived under the help of the Kronecker product and the state feedback control method. Finally, two numerical examples are provided to verify the correctness of the derived criteria.