Exponentially Clustered Synchronization of a Stochastic Complex Network with Reaction–Diffusion Terms and Time Delays via a Pinning Boundary Control

A pinning boundary control strategy that can achieve the exponentially clustered synchronization of a specific class of complex networks is developed. Firstly, the studied model captures the essential features of networks, including spatial dependence, stochastic switching, noise perturbation, and time delays. Secondly, the proposed control algorithm can save the implementation cost and overcome environmental constraint by acting on the boundary of a few nodes. Thirdly, an average state related to the directed topology of the nodes in the same cluster is calculated as the target network. Finally, nonlinear simulations show that the proposed controller can solve the cluster synchronization of a directed coupled reaction–diffusion neural network with Markovian switching, stochastic noise and time delay.