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In this paper, we focus on the pinning exponential synchronisation and passivity of coupled reaction–diffusion neural networks (CRDNNs) with and without parametric uncertainties, respectively. On the one hand, with the help of designed nonlinear pinning controllers and Lyapunov functional method, sufficient conditions are established to let the CRDNNs with hybrid coupling and mixed time-varying delays realise exponential synchronisation and passivity. On the other hand, considering that the external perturbations may lead the reaction–diffusion neural networks (RDNNs) parameters to containing uncertainties, the robust pinning exponential synchronisation and robust pinning passivity for coupled delayed RDNNs with parametric uncertainties are investigated by designing appropriate pinning control strategies. Finally, the effectiveness of the theoretical results are substantiated by the two given numerical examples. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of two kinds of coupled neural networks with different dimensions for input and output vectors, that is, the case with and without time-varying delay. On one side, we analyse the passivity of these coupled neural networks by employing some inequality techniques and a Lyapunov functional approach. On the other side, by designing appropriate pinning control schemes, several conditions are derived, which can make sure that the considered networks are passivity. Finally, numerical examples are given to confirm the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]