Recovering structures of complex dynamical networks based on generalized outer synchronization

The topological structures of complex networks play a crucial role in determining their evolutionary mechanisms and functional behaviors, and may have significant consequences for many real-world applications. Many researchers focused on the geometric features, collective behaviors and control of complex networks provided with precisely known structures. However, the exact topology of a network is usually unknown or uncertain in practical situations. Therefore, accurate and timely topology identification is of great necessity and importance. This paper presents a novel scheme for topology identification. Specifically, an auxiliary complex network with a very general form is constructed and some adaptive controllers are designed to recover the topology of the considered network upon generalized outer synchronization. Different from previous schemes, the network constructed can be composed of any kind of nodes. If the network with an unknown topology has very complicated node dynamics or a high node dimension, one can construct a response network consisting of nodes with much simpler dynamics, which is very practical for circuit design. The effectiveness of the theoretical findings has been illustrated by three numerical examples. This work provides a convenient approach to recovering network topology, which can facilitate the selection of practical circuits and reduce application costs.