Mechanistic modelling of viral spreading on empirical social network and popularity prediction.

Online social networks are becoming major platforms for people to exchange opinions and information. While spreading models have been used to study the dynamics of spreading on social networks, the actual spreading mechanism on social networks may be different from these previous models due to users' limited attention and heterogeneous interests. The tractability of the spreading process in social networks allows us to develop a detailed and realistic model accounting for these factors.

Importance of small-degree nodes in assortative networks with degree-weight correlations.

It has been known that assortative network structure plays an important role in spreading dynamics for unweighted networks. Yet its influence on weighted networks is not clear, in particular when weight is strongly correlated with the degrees of the nodes as we empirically observed in Twitter. Here we use the self-consistent probability method and revised nonperturbative heterogenous mean-field theory method to investigate this influence on both susceptible-infective-recovered (SIR) and susceptible-infective-susceptible (SIS) spreading dynamics.

Socioecological regime shifts in the setting of complex social interactions.

The coupling between social and ecological system has become more ubiquitous and predominant in the current era. The strong interaction between these systems can bring about regime shifts which in the extreme can lead to the collapse of social cooperation and the extinction of ecological resources. In this paper, we study the occurrence of such regime shifts in the context of a coupled social-ecological system where social cooperation is established by means of sanction that punishes local selfish act and promotes norms that prescribe nonexcessive resource extraction.

Exact solution for first-order synchronization transition in a generalized Kuramoto model.

First-order, or discontinuous, synchronization transition, i.e. an abrupt and irreversible phase transition with hysteresis to the synchronized state of coupled oscillators, has attracted much attention along the past years.

From sparse to dense and from assortative to disassortative in online social networks.

Inspired by the analysis of several empirical online social networks, we propose a simple reaction-diffusion-like coevolving model, in which individuals are activated to create links based on their states, influenced by local dynamics and their own intention. It is shown that the model can reproduce the remarkable properties observed in empirical online social networks; in particular, the assortative coefficients are neutral or negative, and the power law exponents γ are smaller than 2. Moreover, we demonstrate that, under appropriate conditions, the model network naturally makes transition(s) from assortative to disassortative, and from sparse to dense in their characteristics.

A coevolving model based on preferential triadic closure for social media networks.

The dynamical origin of complex networks, i.e., the underlying principles governing network evolution, is a crucial issue in network study.

Origin of chaotic transients in excitatory pulse-coupled networks.

We develop an approach to understanding long chaotic transients in networks of excitatory pulse-coupled oscillators. Our idea is to identify a class of attractors, sequentially active firing (SAF) attractors, in terms of the temporal event structure of firing and receipt of pulses. Then all attractors can be classified into two groups: SAF attractors and non-SAF attractors.

Epidemic spreading induced by diversity of agents' mobility.

In this paper, we study the impact of the preference of an individual for public transport on the spread of infectious disease, through a quantity known as the public mobility. Our theoretical and numerical results based on a constructed model reveal that if the average public mobility of the agents is fixed, an increase in the diversity of the agents' public mobility reduces the epidemic threshold, beyond which an enhancement in the rate of infection is observed. Our findings provide an approach to improve the resistance of a society against infectious disease, while preserving the utilization rate of the public transportation system.

Controlling complex networks: how much energy is needed?

The outstanding problem of controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs as well. We address the physically important issue of the energy required for achieving control by deriving and validating scaling laws for the lower and upper energy bounds. These bounds represent a reasonable estimate of the energy cost associated with control, and provide a step forward from the current research on controllability toward ultimate control of complex networked dynamical systems.

Competition between intra-community and inter-community synchronization and relevance in brain cortical networks.

In this paper the effects of inter-community links on the synchronization performance of community networks, especially on the competition between individual community and the whole network, are studied in detail. The study is organized from two aspects: the number or portion of inter-community links and the connection strategy of inter-community links between different communities. A critical point is found in the competition of global network and individual communities.

Onset of synchronization in weighted complex networks: the effect of weight-degree correlation.

By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kind of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network.

Evolution of functional subnetworks in complex systems.

Links in a realistic network may have different functions, which makes the network virtually a combination of some small-size functional subnetworks. Here, by a model of coupled phase oscillators, we investigate how such functional subnetworks are evolved and developed according to the network structure and dynamics. In particular, we study the case of evolutionary clustered networks in which the function type of each link (attractive or repulsive coupling) is adaptively updated according to the local network dynamics.

Onset of synchronization in complex gradient networks.

Recently, it has been found that the synchronizability of a scale-free network can be enhanced by introducing some proper gradient in the coupling. This result has been obtained by using eigenvalue-spectrum analysis under the assumption of identical node dynamics. Here we obtain an analytic formula for the onset of synchronization by incorporating the Kuramoto model on gradient scale-free networks.

Multiple effects of gradient coupling on network synchronization.

Recent studies have shown that the synchronizability of complex networks can be significantly improved by gradient or asymmetric couplings, and increase of the gradient strength could enhance the network synchronizability monotonically. Here we argue and demonstrate that, for a typical complex network, there could be an optimal gradient where the maximum network synchronizability is achieved. That is, large gradient may deteriorate synchronization.

Transition to global synchronization in clustered networks.

A clustered network is characterized by a number of distinct sparsely linked subnetworks (clusters), each with dense internal connections. Such networks are relevant to biological, social, and certain technological networked systems. For a clustered network the occurrence of global synchronization, in which nodes from different clusters are synchronized, is of interest.

Model-based detector and extraction of weak signal frequencies from chaotic data.

Detecting a weak signal from chaotic time series is of general interest in science and engineering. In this work we introduce and investigate a signal detection algorithm for which chaos theory, nonlinear dynamical reconstruction techniques, neural networks, and time-frequency analysis are put together in a synergistic manner. By applying the scheme to numerical simulation and different experimental measurement data sets (Henon map, chaotic circuit, and NH(3) laser data sets), we demonstrate that weak signals hidden beneath the noise floor can be detected by using a model-based detector.

Optimization of synchronization in gradient clustered networks.

We consider complex clustered networks with a gradient structure, where the sizes of the clusters are distributed unevenly. Such networks describe actual networks in biophysical systems and in technological applications more closely than the previous models. Theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field, but only when the gradient field points from large to small clusters.

Enhancing synchronization based on complex gradient networks.

The ubiquity of scale-free networks in nature and technological applications and the finding that such networks may be more difficult to synchronize than homogeneous networks pose an interesting phenomenon for study in network science. We argue and demonstrate that, in the presence of some proper gradient fields, scale-free networks can be more synchronizable than homogeneous networks. The gradient structure can in fact arise naturally in any weighted and asymmetrical networks; based on this we propose a coupling scheme that permits effective synchronous dynamics on the network.

Oscillations of complex networks.

A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how such quantities respond to sudden changes caused by attacks or disturbances in recoverable networks, i.e.

Characterization of noise-induced strange nonchaotic attractors.

Strange nonchaotic attractors (SNAs) were previously thought to arise exclusively in quasiperiodic dynamical systems. A recent study has revealed, however, that such attractors can be induced by noise in nonquasiperiodic discrete-time maps or in periodically driven flows. In particular, in a periodic window of such a system where a periodic attractor coexists with a chaotic saddle (nonattracting chaotic invariant set), none of the Lyapunov exponents of the asymptotic attractor is positive.

Effect of resonant-frequency mismatch on attractors.

Resonant perturbations are effective for harnessing nonlinear oscillators for various applications such as controlling chaos and inducing chaos. Of physical interest is the effect of small frequency mismatch on the attractors of the underlying dynamical systems. By utilizing a prototype of nonlinear oscillators, the periodically forced Duffing oscillator and its variant, we find a phenomenon: resonant-frequency mismatch can result in attractors that are nonchaotic but are apparently strange in the sense that they possess a negative Lyapunov exponent but its information dimension measured using finite numerics assumes a fractional value.

Effect of noise on generalized chaotic synchronization.

When two characteristically different chaotic oscillators are coupled, generalized synchronization can occur. Motivated by the phenomena that common noise can induce and enhance complete synchronization or phase synchronization in chaotic systems, we investigate the effect of noise on generalized chaotic synchronization. We develop a phase-space analysis, which suggests that the effect can be system dependent in that common noise can either induce/enhance or destroy generalized synchronization.

Public-key encryption based on generalized synchronization of coupled map lattices.

Currently used public-key cryptosystems are based on difficulties in solving certain numeric theoretic problems, in which the way to predict the private key from the knowledge of the public key is computationally infeasible. Here we propose a method of constructing public-key cryptosystems by generalized synchronization of coupled map lattices, in which the difficulty in predicting the synchronous function is used as the trap-door function to deduce the private key from the public key. In specific, we implement this idea on the method of "Merkle's puzzles," and find that, incorporated with the chaotic dynamics, this traditional method is equipped with some new features and can be practical in certain situations.

Strange nonchaotic attractors in random dynamical systems.

Whether strange nonchaotic attractors (SNAs) can occur typically in dynamical systems other than quasiperiodically driven systems has long been an open question. Here we show, based on a physical analysis and numerical evidence, that robust SNAs can be induced by small noise in autonomous discrete-time maps and in periodically driven continuous-time systems. These attractors, which are relevant to physical and biological applications, can thus be expected to occur more commonly in dynamical systems than previously thought.

Shadowability of statistical averages in chaotic systems.

We ask whether statistical averages in chaotic systems can be computed or measured reliably under the influence of noise. Situations are identified where the invariance of such averages breaks down as the noise amplitude increases through a critical level. An algebraic scaling law is obtained which relates the change of the averages to the noise variation.