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An urgent problem in controlling COVID-19 spreading is to understand the role of undocumented infection. We develop a five-state model for COVID-19, taking into account the unique features of the novel coronavirus, with key parameters determined by the government reports and mathematical optimization. Tests using data from China, South Korea, Italy, and Iran indicate that the model is capable of generating accurate prediction of the daily accumulated number of confirmed cases and is entirely suitable for real-time prediction. The drastically disparate testing and diagnostic standards/policies among different countries lead to large variations in the estimated parameter values such as the duration of the outbreak, but such uncertainties have little effect on the occurrence time of the inflection point as predicted by the model, indicating its reliability and robustness. Model prediction for Italy suggests that insufficient government action leading to a large fraction of undocumented infection plays an important role in the abnormally high mortality in that country. With the data currently available from United Kingdom, our model predicts catastrophic epidemic scenarios in the country if the government did not impose strict travel and social distancing restrictions. A key finding is that, if the percentage of undocumented infection exceeds a threshold, a non-negligible hidden population can exist even after the the epidemic has been deemed over, implying the likelihood of future outbreaks should the currently imposed strict government actions be relaxed. This could make COVID-19 evolving into a long-term epidemic or a community disease a real possibility, suggesting the necessity to conduct universal testing and monitoring to identify the hidden individuals., Comment: 20 pages, 7 figures

Non-Markovian spontaneous recovery processes with a time delay (memory) are ubiquitous in the real world. How does the non-Markovian characteristic affect failure propagation in complex networks? We consider failures due to internal causes at the nodal level and external failures due to an adverse environment, and develop a pair approximation analysis taking into account the two-node correlation. In general, a high failure stationary state can arise, corresponding to large-scale failures that can significantly compromise the functioning of the network. We uncover a striking phenomenon: memory associated with nodal recovery can counter-intuitively make the network more resilient against large-scale failures. In natural systems, the intrinsic non-Markovian characteristic of nodal recovery may thus be one reason for their resilience. In engineering design, incorporating certain non-Markovian features into the network may be beneficial to equipping it with a strong resilient capability to resist catastrophic failures., Comment: 13 pages, 8 figures, Supplementary Information

Information spreading has been studied for decades, but its underlying mechanism is still under debate, especially for those ones spreading extremely fast through Internet. By focusing on the information spreading data of six typical events on Sina Weibo, we surprisingly find that the spreading of modern information shows some new features, i.e. either extremely fast or slow, depending on the individual events. To understand its mechanism, we present a Susceptible-Accepted-Recovered (SAR) model with both information sensitivity and social reinforcement. Numerical simulations show that the model can reproduce the main spreading patterns of the six typical events. By this model we further reveal that the spreading can be speeded up by increasing either the strength of information sensitivity or social reinforcement. Depending on the transmission probability and information sensitivity, the final accepted size can change from continuous to discontinuous transition when the strength of the social reinforcement is large. Moreover, an edge-based compartmental theory is presented to explain the numerical results. These findings may be of significance on the control of information spreading in modern society., Comment: 10 pages, 8 figures

The study of epidemic spreading on populations of networked individuals has seen recently a great deal of significant progresses. A common point of all past studies is, however, that there is only one peak of infected density in each single epidemic spreading episode. At variance, real data from different cities over the world suggest that, besides a major single peak trait of infected density, a finite probability exists for a pattern made of two (or multiple) peaks. We show that such a latter feature is fully distinctive of a multilayered network of interactions, and reveal that actually a two peaks pattern emerges from different time delays at which the epidemic spreads in between the two layers. Further, we show that essential ingredients are different degree distributions in the two layers and a weak coupling condition between the layers themselves. Moreover, an edge-based theory is developed which fully explains all numerical results. Our findings may therefore be of significance for protecting secondary disasters of epidemics, which are definitely undesired in real life., Comment: 30 pages, 4 figures

Recently, the explosive phase transitions, such as explosive percolation and explosive synchronization, have attracted extensive research interest. So far, most existing works investigate Kuramoto-type models, where only phase variables are involved. Here, we report the occurrence of explosive oscillation quenching in a system of coupled Stuart-Landau oscillators that incorporates both phase and amplitude dynamics. We observe three typical scenarios with distinct microscopic mechanism of occurrence, i.e., ordinary, hierarchical, and cluster explosive oscillation death, corresponding to different frequency distributions of oscillators, respectively. We carry out theoretical analyses and obtain the backward transition point, which is shown to be independent of the specific frequency distributions. Numerical results are consistent with the theoretical prediction.

In this work, we study the dynamical robustness in a system consisting of both active and inactive oscillators. We analytically show that the dynamical robustness of such system is determined by the cross link density between active and inactive subpopulations, which depends on the specific process of inactivation. It is the multi-valued dependence of the cross link density on the control parameter, i.e., the ratio of inactive oscillators in the system, that leads to the fluctuation of the critical points. We further investigate how different network topologies and inactivation strategies affect the fluctuation. Our results explain why the fluctuation is more obvious in heterogeneous networks than in homogeneous ones, and why the low-degree nodes are crucial in terms of dynamical robustness. The analytical results are supported by numerical verifications.

It has been found that contrarian oscillators usually take a negative role in the collective behaviors formed by conformist oscillators. However, experiments revealed that it is also possible to achieve a strong coherence even when there are contrarians in the system such as neuron networks with both excitable and inhibitory neurons. To understand the underlying mechanism of this abnormal phenomenon, we here consider a complex network of coupled Kuramoto oscillators with mixed positive and negative couplings and present an efficient approach, i.e. tit-for-tat strategy, to suppress the negative role of contrarian oscillators in synchronization and thus increase the order parameter of synchronization. Two classes of contrarian oscillators are numerically studied and a brief theoretical analysis is provided to explain the numerical results.

Global and partial synchronization are the two distinctive forms of synchronization in coupled oscillators and have been well studied in the past decades. Recent attention on synchronization is focused on the chimera state (CS) and explosive synchronization (ES), but little attention has been paid to their relationship. We here study this topic by presenting a model to bridge these two phenomena, which consists of two groups of coupled oscillators and its coupling strength is adaptively controlled by a local order parameter. We find that this model displays either CS or ES in two limits. In between the two limits, this model exhibits both CS and ES, where CS can be observed for a fixed coupling strength and ES appears when the coupling is increased adiabatically. Moreover, we show both theoretically and numerically that there are a variety of CS basin patterns for the case of identical oscillators, depending on the distributions of both the initial order parameters and the initial average phases. This model suggests a way to easily observe CS, in contrast to others models having some (weak or strong) dependence on initial conditions.

Chimera states have been studied in 1D arrays, and a variety of different chimera states have been found using different models. Research has recently been extended to 2D arrays but only to phase models of them. Here, we extend it to a nonphase model of 2D arrays of neurons and focus on the influence of nonlocal coupling. Using extensive numerical simulations, we find, surprisingly, that this system can show most types of previously observed chimera states, in contrast to previous models, where only one or a few types of chimera states can be observed in each model. We also find that this model can show some special chimera-like patterns such as gridding and multicolumn patterns, which were previously observed only in phase models. Further, we present an effective approach, i.e., removing some of the coupling links, to generate heterogeneous coupling, which results in diverse chimera-like patterns and even induces transformations from one chimera-like pattern to another.

Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean fields. We derive stability properties of the incoherent state and find traveling wave solutions with different locking patterns; stability properties of these waves are found numerically. Mostly nontrivial states appear when the two fields compete, i.e. one tends to synchronize oscillators while the other one desynchronizes them. Here we identify normal branches which bifurcate from the incoherent state in a usual way, and anomalous branches, appearance of which cannot be described as a bifurcation. Furthermore, hybrid branches combining properties of both are described. In the situations where no stable traveling wave exists, modulated quasiperiodic in time dynamics is observed. Our results indicate that a competition between two coupling channels can lead to a complex system behavior, providing a potential generalized framework for understanding of complex phenomena in natural oscillatory systems.

Epidemic spreading has been studied for a long time and most of them are focused on the growing aspect of a single epidemic outbreak. Recently, we extended the study to the case of recurrent epidemics (Sci. Rep. {\bf 5}, 16010 (2015)) but limited only to a single network. We here report from the real data of coupled regions or cities that the recurrent epidemics in two coupled networks are closely related to each other and can show either synchronized outbreak phase where outbreaks occur simultaneously in both networks or mixed outbreak phase where outbreaks occur in one network but do not in another one. To reveal the underlying mechanism, we present a two-layered network model of coupled recurrent epidemics to reproduce the synchronized and mixed outbreak phases. We show that the synchronized outbreak phase is preferred to be triggered in two coupled networks with the same average degree while the mixed outbreak phase is preferred for the case with different average degrees. Further, we show that the coupling between the two layers is preferred to suppress the mixed outbreak phase but enhance the synchronized outbreak phase. A theoretical analysis based on microscopic Markov-chain approach is presented to explain the numerical results. This finding opens a new window for studying the recurrent epidemics in multi-layered networks., Comment: 12 pages, 6 figures

Two decades ago, a phenomenon resembling Landau damping was described in the synchronization of globally coupled oscillators: the evidence of a regime where the order parameter decays when linear theory predicts neutral stability for the incoherent state. We here show that such an effect is far more generic, as soon as phase oscillators couple to their mean field according to their natural frequencies, being then grouped into two distinct populations of conformists and contrarians. We report the analytical solution of this latter situation, which allows determining the critical coupling strength and the stability of the incoherent state, together with extensive numerical simulations that fully support all theoretical predictions. The relevance of our results is discussed in relationship to collective phenomena occurring in polarized social systems.

Explosive synchronization (ES) is nowadays a hot topic of interest in nonlinear science and complex networks. So far, it is conjectured that ES is rooted in the setting of specific microscopic correlation features between the natural frequencies of the networked oscillators and their effective coupling strengths. We show that ES, in fact, is far more general, and can occur in adaptive and multilayer networks also in the absence of such correlation properties. Precisely, we first report evidence of ES in the absence of correlation for networks where a fraction f of the nodes have links adaptively controlled by a local order parameter, and then we extend the study to a variety of two-layer networks with a fraction f of their nodes coupled each other by means of dependency links. In this latter case, we even show that ES sets in, regardless of the differences in the frequency distribution and/or in the topology of connections between the two layers. Finally, we provide a rigorous, analytical, treatment to properly ground all the observed scenario, and to facilitate the understanding of the actual mechanisms at the basis of ES in real-world systems.

Spontaneous explosive emergent behavior takes place in heterogeneous networks when the frequencies of the nodes are positively correlated to the node degree. A central feature of such explosive transitions is a hysteretic behavior at the transition to synchronization. We unravel the underlying mechanisms and show that the dynamical origin of the hysteresis is a change of basin of attraction of the synchronization state. Our findings hold for heterogeneous networks with star graph motifs such as scale free networks, and hence reveal how microscopic network parameters such as node degree and frequency affect the global network properties and can be used for network design and control., Comment: 5 pages, 4 figures

Complex network approaches have been recently developed as an alternative framework to study the statistical features of time-series data. We perform a visibility-graph analysis on both the daily and monthly sunspot series. Based on the data, we propose two ways to construct the network: one is from the original observable measurements and the other is from a negative-inverse-transformed series. The degree distribution of the derived networks for the strong maxima has clear non-Gaussian properties, while the degree distribution for minima is bimodal. The long-term variation of the cycles is reflected by hubs in the network which span relatively large time intervals. Based on standard network structural measures, we propose to characterize the long-term correlations by waiting times between two subsequent events. The persistence range of the solar cycles has been identified over 15\,--\,1000 days by a power-law regime with scaling exponent $\gamma = 2.04$ of the occurrence time of the two subsequent and successive strong minima. In contrast, a persistent trend is not present in the maximal numbers, although maxima do have significant deviations from an exponential form. Our results suggest some new insights for evaluating existing models. The power-law regime suggested by the waiting times does indicate that there are some level of predictable patterns in the minima., Comment: 18 pages, 11 figures. Solar Physics, 2013

We study vibrational energy transport in a quasi 1-D harmonic chain with both longitudinal and transverse vibrations. We demonstrate via both numerical simulation and theoretic analysis that for 1-D atomic chain connected by 3D harmonic springs, the coefficient of heat conduction changes it continuously with its lattice constant, indicating the qualitative difference from the corresponding 1-D case where the coefficient is independent of the lattice constant., Comment: 4 pages, 4 figures

Different routing strategies may result in different behaviors of traffic on internet. We analyze the correlation of traffic data for three typical routing strategies by the detrended fluctuation analysis (DFA) and find that the degree of correlation of the data can be divided into three regions, i.e., weak, medium, and strong correlation. The DFA scalings are constants in both the regions of weak and strong correlation but monotonously increase in the region of medium correlation. We suggest that it is better to consider the traffic on complex network as three phases, i.e., the free, buffer, and congestion phase, than just as two phases believed before, i.e., the free and congestion phase., Comment: 4 pages, 4 figures

We present an efficient routing approach for delivering packets in complex networks. On delivering a message from a node to a destination, a node forwards the message to a neighbor by estimating the waiting time along the shortest path from each of its neighbors to the destination. This projected waiting time is dynamical in nature and the path through which a message is delivered would be adapted to the distribution of messages in the network. Implementing the approach on scale-free networks, we show that the present approach performs better than the shortest-path approach and another approach that takes into account of the waiting time only at the neighboring nodes. Key features in numerical results are explained by a mean field theory. The approach has the merit that messages are distributed among the nodes according to the capabilities of the nodes in handling messages., Comment: 6 pages, 4 figures

The heat conduction in simple networks consisting of different one dimensional nonlinear chains is studied. We find that the coupling between chains has different function in heat conduction compared with that in electric current. This might find application in controlling heat flow in complex networks., Comment: 5 pages, 5 figures

We study the condensation phenomenon in a zero range process on weighted scale-free networks in order to show how the weighted transport influences the particle condensation. Instead of the approach of grand canonical ensemble which is generally used in a zero range process, we introduce an alternate approach of the mean field equations to study the dynamics of particle transport. We find that the condensation on scale-free network is easier to occur in the case of weighted transport than in the case of weight-free. In the weighted transport, especially, a dynamical condensation is even possible for the case of no interaction among particles, which is impossible in the case of weight-free., Comment: 6 pages, 4 figures