Edge-Based Synchronization Control Criteria of Complex Dynamical Networks with Reaction–Diffusions

Abstract

This research investigates the edge-based asymptotic synchronization of delayed complex dynamical networks with reaction–diffusions and by an edge-based adaptive pinning control technique. Sufficient conditions for reaction–diffusion networks to realize synchronization are provided by Green’s formula, Wirtinger inequality, inequality analysis techniques, and contradiction methods. The results show that network synchronization can be achieved by pinning any edge of the network (the choice of edge is arbitrary), which greatly reduces the difficulty of control. Lastly, a series of numerical examples illustrating the theoretical findings is provided.

Keywords

• complex networks
• asymptotical synchronization
• edge-based adaptive pinning control
• reaction–diffusion terms
• delays