Inferring topologies via driving-based generalized synchronization of two-layer networks

TL;DR

This paper introduces a novel method for inferring the topology of complex dynamical networks using generalized synchronization in a two-layer network framework, accounting for communication delays and perturbations.

Contribution

It proposes an adaptive control approach based on the LaSalle invariance principle to recover unknown network topologies through synchronization, applicable to high-dimensional and complex systems.

Findings

Effective topology inference demonstrated through numerical simulations.

Method accommodates communication delays and perturbations.

Applicable to subnetworks and hidden source localization.

Abstract

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.