Recovering Network Structures with Time-Varying Nodal Parameters

Complex networks with time-varying nodal parameters are of considerable interest and significance in many areas of science and engineering. Reconstructing networks with unknown but continuously bounded time-varying nodal parameters from limited measured information is desirable and of significant interest for using and controlling these networks. Based on the Lasso method and the Taylor expansion approximation, we develop an efficient and feasible, completely data-driven approach to predicting the structures of networks with unknown but continuously bounded time-varying nodal parameters in the presence or absence of noise. In particular, the reconstruction framework is implemented on several different kinds of artificial, two-layer and real complex networks composed of various parameter-varying nodal dynamics. Through numerical simulations, we demonstrate that, networks structures can be fully reconstructed with limited available information and presence or absence of noise, though systemic parameters are continuously time-varying. In addition, our method is also applicable to structure identification of multilayer networks as well as networks with constant nodal parameters. We expect our method to be useful in addressing issues of significantly current concern in the information era, natural networks, and large-scale multilayer networks.