Synchronisation in complex networks via the input–output function of dynamic relay links

In this paper, the synchronisation problem for a category of complex dynamical networks (CDNs) incorporating dynamic relay links (DRLs) with input–output function is investigated. In contrast to the current literature, this paper introduces the concept of a relay-conversion relationship to describe the connections between nodes and proposes a complex network model composed of a DRL subsystem and a node subsystem. In this model, these two subsystems are coupled by their respective outputs, which demonstrates the unique input–output characteristic and function of the DRLs. Subsequently, to realise node synchronisation, the node controller and the DRL coupling term are designed based on Lyapunov stability theory. Furthermore, under the coupling effect of the node subsystem, the DRL synchronisation is also achieved while the nodes achieve synchronisation. Finally, by using a numerical simulation example, the viability of the control scheme proposed in this paper is confirmed.