General decay synchronization and [formula omitted] synchronization of spatial diffusion coupled delayed reaction–diffusion neural networks

Abstract

This paper deals with the general decay synchronization (GDS) and general decay H∞ synchronization (GDHS) problems for spatial diffusion coupled delayed reaction–diffusion neural networks (SDCDRDNNs) without and with uncertain parameters respectively. First, based on the ψ-type stability and ψ-type function, the concept of GDS is generalized to include general robust decay synchronization (GRDS) and GDHS. Then, by exploiting a nonlinear controller and different types of inequality techniques, some verifiably sufficient conditions ensuring the GDS and GDHS of SDCDRDNNs (without and with uncertain parameters) are derived. Finally, two simulative examples are provided to demonstrate the validity of the synchronization results obtained.