Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms

Abstract

In this paper, a class of fractional complex networks with impulses and reaction−diffusion terms is introduced and studied. Meanwhile, a class of more general network structures is considered, which consists of an instant communication topology and a delayed communication topology. Based on the Lyapunov method and linear matrix inequality techniques, some sufficient criteria are obtained, ensuring adaptive pinning synchronization of the network under a designed adaptive control strategy. In addition, a pinning scheme is proposed, which shows that the nodes with delayed communication are good candidates for applying controllers. Finally, a numerical example is given to verify the validity of the main results.

Keywords

• fractional complex networks
• adaptive control
• pinning synchronization
• time-varying delays
• impulses
• reaction–diffusion terms