Hybrid adaptive synchronization strategy for linearly coupled reaction–diffusion neural networks with time-varying coupling strength

Abstract In this article, the adaptive synchronization control for an array of coupled reaction diffusion neural networks with time-varying coupling strength and delays is considered. A novel hybrid adaptive learning law consists of discrete updating law for the unknown time-varying coupling coefficient and continuous adaptive law for the unknown time-invariant parameter is derived, which extends the adaptive synchronization control for the constant coupling coefficient to the time-varying one. Through constructing a novel Lyapunov–Krasovskii functional, the synchronization controller and criterion are presented. Furthermore, to take the disturbance into consideration, the H ∞ synchronization criterion is presented, also. Finally, a numerical example is given and some comparisons are performed to demonstrate the effectiveness of the synchronization strategies.