  The interaction topology among the constituents of a complex network plays a
crucial role in the network's evolutionary mechanisms and functional behaviors.
However, some network topologies are usually unknown or uncertain. Meanwhile,
coupling delay are ubiquitous in various man-made and natural networks. Hence,
it is necessary to gain knowledge of the whole or partial topology of a complex
dynamical network by taking into consideration communication delay. In this
paper, topology identification of complex dynamical networks is investigated
via generalized synchronization of a two-layer network. Particularly, based on
the LaSalle-type invariance principle of stochastic differential delay
equations, an adaptive control technique is proposed by constructing an
auxiliary layer and designing proper control input and updating laws so that
the unknown topology can be recovered upon successful generalized
synchronization. Numerical simulations are provided to illustrate the
effectiveness of the proposed method. The technique provides a certain
theoretical basis for topology inference of complex networks. In particular,
when the considered network is composed of systems with high-dimension or
complicated dynamics, a simpler response layer can be constructed, which is
conducive to circuit design. Moreover, it is practical to take into
consideration perturbations caused by control input. Finally, the method is
applicable to infer topology of a subnetwork embedded within a complex system
and locate hidden sources. We hope the results can provide basic insight into
further research endeavors on understanding practical and economical topology
inference of networks.
