Topology inference of uncertain complex dynamical networks and its applications in hidden nodes detection

The topological structure of a complex dynamical network plays a vital role in determining the network’s evolutionary mechanisms and functional behaviors, thus recognizing and inferring the network structure is of both theoretical and practical significance. Although various approaches have been proposed to estimate network topologies, many are not well established to the noisy nature of network dynamics and ubiquity of transmission delay among network individuals. This paper focuses on topology inference of uncertain complex dynamical networks. An auxiliary network is constructed and an adaptive scheme is proposed to track topological parameters. It is noteworthy that the considered network model is supposed to contain practical stochastic perturbations, and noisy observations are taken as control inputs of the constructed auxiliary network. In particular, the control technique can be further employed to locate hidden sources (or latent variables) in networks. Numerical examples are provided to illustrate the effectiveness of the proposed scheme. In addition, the impact of coupling strength and coupling delay on identification performance is assessed. The proposed scheme provides engineers with a convenient approach to infer topologies of general complex dynamical networks and locate hidden sources, and the detailed performance evaluation can further facilitate practical circuit design.     

The changes on synchronizing ability of coupled networks from ring networks to chain networks

In this paper, two different ring networks with unidirectional couplings and with bidirectional couplings were discussed by theoretical analysis. It was found that the effects on synchronizing ability of the two different structures by cutting a link are completely opposite. The synchronizing ability will decrease if the change is from bidirectional ring to bidirectional chain. Moreover, the change on synchro- nizing ability will be four times if the number of N is large enough. However, it will increase obviously from unidirectional ring to unidirectional chain. It will be N 2/(2π2) times if the number of N is large enough. The numerical simulations confirm the conclusion in quality. This paper also discusses the effects on synchronization by adding one link with different length d to these two different structures. It can be seen that the effects are different. Theoretical results are accordant to numerical simulations. Synchronization is an essential physics problem. These results pro- posed in this paper have some important reference meanings on the real world networks, such as the bioecological system networks, the designing of the circuit, etc.     

Recovering unknown topology in a two-layer multiplex network: One layer infers the other layer

There have been increasing interests in studying multiplex dynamical networks recently. This paper focuses on topology identification of two-layer multiplex networks with peer-to-peer interlayer couplings. For a two-layer network model in which different layers have different coupling patterns, we propose novel methods to recover unknown topological structure of one layer, using the information of the other layer known as a prior. The proposed methods make full use of the measured evolutional states of the multiplex network itself, and treat the layer with a known structure as an auxiliary layer which is designed to identify the unknown topological layer. Compared with the traditional synchronization-based identification method, the proposed methods are in no need of constructing an additional auxiliary network to identify the unknown topological layer, and thus greatly reduce the cost of topology identification. Finally, numerical simulations validate the effectiveness of the proposed methods.

     

A threshold effect of coupling delays on intra-layer synchronization in duplex networks

This paper investigates the impact of inter-layer coupling functions and intra-layer coupling delays on intra-layer synchronization regions and sychronizability. It is found that the inter-layer coupling functions have great influence on intra-layer synchronization regions, as well as on the intra-layer synchronizability. In particular, there exists an inter-layer coupling function such that the inter-layer coupling strength neither improves nor weakens the intra-layer synchronizability. Furthermore, no matter which one of three inter-layer coupling functions is chosen, a small intra-layer delay always keeps the intra-layer synchronized regions almost unchanged, implying that the small delay neither enhances nor suppresses the intra-layer synchronizability. At the same time the delay greatly frustrates the synchronizability in each layer when it is greater than some threshold. Our results may have potential applications for interconnected technological networks where communication delays are inevitably present.