Fiedler value: The cumulated dynamical contribution value of all edges in a complex network.

Fiedler value, as the minimal real part of (or the minimal) nonzero Laplacian eigenvalue, garners significant attention as a metric for evaluating network topology and its dynamics. In this paper, we address the quantification relation between Fiedler value and each edge in a directed complex network, considering undirected networks as a special case. We propose an approach to measure the dynamical contribution value of each edge.

Searching for Key Cycles in a Complex Network.

Searching for key nodes and edges in a network is a long-standing problem. Recently cycle structure in a network has received more attention. Is it possible to propose a ranking algorithm for cycle importance? We address the problem of identifying the key cycles of a network.

Occurrence of super-diffusion in two-layer networks.

Super-diffusion is a phenomenon that can be observed in multilayer networks, which describes that the diffusion in a multilayer network is faster than that in the fastest individual layer. In most studies of super-diffusion on two-layer networks, many researchers have focused on the overlap of edges in the two layers and the mode of interlayer connectivity. We discover that the occurrence of super-diffusion in two-layer networks is not necessarily related to the overlap degree.

Superdiffusion induced by complete structure in multiplex networks.

After the groundbreaking work by Gómez et al., the superdiffusion phenomenon on multiplex networks begins to attract researchers' attention. The emergence of superdiffusion means that the time scale of the diffusion process of the multiplex network is shorter than that of each layer.

Adaptive Exponential Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay.

In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem.

Synchronizability of two-layer correlation networks.

This study investigates the synchronizability of a typical type of two-layer correlation networks formed by two regular networks interconnected with two interlayer linking patterns, namely, positive correlation (PC) and negative correlation (NC). To analyze the network's stability, we consider the analytical expressions of the smallest non-zero and largest eigenvalues of the (weighted) Laplacian matrix as well as the linking strength and the network size for two linking patterns. According to the master stability function, the linking patterns, the linking strength, and the network size associated with two typical synchronized regions exhibit a profound influence on the synchronizability of the two-layer networks.

Synchronizability of double-layer dumbbell networks.

Synchronization of multiplex networks has been a topical issue in network science. Dumbbell networks are very typical structures in complex networks which are distinguished from both regular star networks and general community structures, whereas the synchronous dynamics of a double-layer dumbbell network relies on the interlink patterns between layers. In this paper, two kinds of double-layer dumbbell networks are defined according to different interlayer coupling patterns: one with the single-link coupling pattern between layers and the other with the two-link coupling pattern between layers.

Superdiffusion criteria on duplex networks.

Diffusion processes widely exist in nature. Some recent papers concerning diffusion processes focus their attention on multiplex networks. Superdiffusion, a phenomenon by which diffusion processes converge to equilibrium faster on multiplex networks than on single networks in isolation, may emerge because diffusion can occur both within and across layers.

The combination of targeted vaccination and ring vaccination.

Complex networks have become an important tool for investigating epidemic dynamics. A widely concerned research field for epidemics is to develop and study mitigation strategies or control measures. In this paper, we devote our attention to ring vaccination and targeted vaccination and consider the combination of them.

Topology Identification of Multilink Complex Dynamical Networks via Adaptive Observers Incorporating Chaotic Exosignals.

Topology identification of complex networks is an important and meaningful research direction. In recent years, the topology identification method based on adaptive synchronization has been developed rapidly. However, a critical shortcoming of this method is that inner synchronization of a network breaks the precondition of linear independence and leads to the failure of topology identification.

Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay.

In this article, we investigate the synchronization of complex networks with general time-varying delay, especially with nondifferentiable delay. In the literature, the time-varying delay is usually assumed to be differentiable. This assumption is strict and not easy to verify in engineering.

The effect of behavior of wearing masks on epidemic dynamics.

Recently, COVID-19 has attracted a lot of attention of researchers from different fields. Wearing masks is a frequently adopted precautionary measure. In this paper, we investigate the effect of behavior of wearing masks on epidemic dynamics in the context of COVID-19.

Statistical and network analysis of 1212 COVID-19 patients in Henan, China.

Background: COVID-19 is spreading quickly all over the world. Publicly released data for 1212 COVID-19 patients in Henan of China were analyzed in this paper.

Methods: Various statistical and network analysis methods were employed.

Cluster synchronization: From single-layer to multi-layer networks.

Cluster synchronization is a very common phenomenon occurring in single-layer complex networks, and it can also be observed in many multilayer networks in real life. In this paper, we study cluster synchronization of an isolated network and then focus on that of the network when it is influenced by an external network. We mainly explore how the influence layer impacts the cluster synchronization of the interest layer in a multilayer network.

Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled Rössler oscillators.

Synchronization phenomena are of broad interest across disciplines and increasingly of interest in a multiplex network setting. For the multiplex network of coupled Rössler oscillators, here we show how the master stability function, a celebrated framework for analyzing synchronization on a single network, can be extended to certain classes of multiplex networks with different intralayer and interlayer coupling functions. We derive three master stability equations that determine, respectively, the necessary regions of complete synchronization, intralayer synchronization, and interlayer synchronization.

A New Method for Topology Identification of Complex Dynamical Networks.

Topology identification of complex dynamical networks received extensive attention in the past decade. Most existing studies rely heavily on the linear independence condition (LIC). We find that a critical step in using this condition is not rigorous.

Synthesis of Diverse Boron-Handled N-Heterocycles via Radical Borylative Cyclization of N-Allylcyanamides.

A synthetic method based on radical borylation/cyclization cascades of N-allylcyanamides was developed to construct diverse boron-substituted N-heterocycles. In the reaction process, the N-heterocyclic carbene-boryl radical underwent a chemo- and regioselective addition to the alkene moiety, followed by cyclization with the N-cyano group. The resulting amide-iminyl radical intermediates underwent further reactions to afford various boron-tethered N-heterocyclic molecules.

Phase synchronization on spatially embedded duplex networks with total cost constraint.

Synchronization on multiplex networks has attracted increasing attention in the past few years. We investigate collective behaviors of Kuramoto oscillators on single layer and duplex spacial networks with total cost restriction, which was introduced by Li . [Phys.

Pinning Synchronization of Multiplex Delayed Networks With Stochastic Perturbations.

As the monoplex network has its limitations in describing the real world, a new framework called the multiplex network is put forward and has received much attention in recent years. This paper focuses on synchronization of the multiplex network with multiple delays and stochastic perturbations. Due to the complexity, pinning control of the multiplex network is of particular interest.

Identifying partial topology of complex dynamical networks via a pinning mechanism.

In this paper, we study the problem of identifying the partial topology of complex dynamical networks via a pinning mechanism. By using the network synchronization theory and the adaptive feedback controlling method, we propose a method which can greatly reduce the number of nodes and observers in the response network. Particularly, this method can also identify the whole topology of complex networks.

Maximizing synchronizability of duplex networks.

We study the synchronizability of duplex networks formed by two randomly generated network layers with different patterns of interlayer node connections. According to the master stability function, we use the smallest nonzero eigenvalue and the eigenratio between the largest and the second smallest eigenvalues of supra-Laplacian matrices to characterize synchronizability on various duplexes. We find that the interlayer linking weight and linking fraction have a profound impact on synchronizability of duplex networks.

Compressive-Sensing-Based Structure Identification for Multilayer Networks.

The coexistence of multiple types of interactions within social, technological, and biological networks has motivated the study of the multilayer nature of real-world networks. Meanwhile, identifying network structures from dynamical observations is an essential issue pervading over the current research on complex networks. This paper addresses the problem of structure identification for multilayer networks, which is an important topic but involves a challenging inverse problem.

Cooperative spreading processes in multiplex networks.

This study is concerned with the dynamic behaviors of epidemic spreading in multiplex networks. A model composed of two interacting complex networks is proposed to describe cooperative spreading processes, wherein the virus spreading in one layer can penetrate into the other to promote the spreading process. The global epidemic threshold of the model is smaller than the epidemic thresholds of the corresponding isolated networks.

Identifying structures of continuously-varying weighted networks.

Identifying network structures from dynamical observations is a fundamental problem currently pervading scientific research on complex systems, as understanding and modeling the structure of a complex network will lead to greater knowledge of its evolutionary mechanisms and to a better understanding of its functional behaviors. Usually, one needs to identify a network's structure through a limited number of observations. Particularly, couplings of many real-world networks are sparse and continuously varying with time.

Driving-based generalized synchronization in two-layer networks via pinning control.

Synchronization of complex networks has been extensively investigated in various fields. In the real world, one network is usually affected by another one but coexists in harmony with it, which can be regarded as another kind of synchronization--generalized synchronization (GS). In this paper, the GS in two-layer complex networks with unidirectional inter-layer coupling via pinning control is investigated based on the auxiliary-system approach.