Passivity and Passivity-Based Synchronization of Switched Coupled Reaction-Diffusion Neural Networks with State and Spatial Diffusion Couplings

The authors investigate the passivity problem of switched coupled reaction-diffusion neural networks (SCRDNNs) with state and spatial diffusion couplings in this paper. For the considered network model, we derive an input strict passivity (ISP) criterion and an output strict passivity (OSP) criterion respectively by constructing an appropriate Lyapunov functional and exploiting Green's formula and some other useful inequalities. Additionally, the authors also establish the relationship between exponential stability and OSP. Moreover, a sufficient condition for achieving synchronization of the considered SCRDNNs with hybrid coupling is presented according to the deduced OSP result and the relationship between exponential stability and OSP. Finally, the correctness of the derived theoretical conclusions is illustrated by two examples with simulation results.