Wen-Xu Wang

Memory-based snowdrift game on networks.

We present a memory-based snowdrift game (MBSG) taking place on networks. We found that, when a lattice is taken to be the underlying structure, the transition of spatial patterns at some critical values of the payoff parameter is observable for both four- and eight-neighbor lattices. The transition points as well as the styles of spatial patterns can be explained by local stability analysis. In sharp contrast to previously reported results, cooperation is promoted by the spatial structure in the MBSG. Interestingly, we found that the frequency of cooperation of the MBSG on a scale-free network peaks at a specific value of the payoff parameter. This phenomenon indicates that properly encouraging selfish behaviors can optimally enhance the cooperation. The memory effects of individuals are discussed in detail and some non-monotonous phenomena are observed on both lattices and scale-free networks. Our work may shed some new light on the study of evolutionary games over networks.

Exact controllability of complex networks

Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems.

General Dynamics of Topology and Traffic on Weighted Technological Networks

For most technical networks, the interplay of dynamics, traffic, and topology is assumed crucial to their evolution. In this Letter, we propose a traffic-driven evolution model of weighted technological networks. By introducing a general strength-coupling mechanism under which the traffic and topology mutually interact, the model gives power-law distributions of degree, weight, and strength, as confirmed in many real networks. Particularly, depending on a parameter W that controls the total weight growth of the system, the nontrivial clustering coefficient C, degree assortativity coefficient r, and degree-strength correlation are all consistent with empirical evidence.

Integrating local static and dynamic information for routing traffic

The efficiency of traffic routing on complex networks can be reflected by two key measurements, i.e., the network capacity and the average travel time of data packets. In this paper we propose a mixing routing strategy by integrating local static and dynamic information for enhancing the efficiency of traffic on scale-free networks. The strategy is governed by a single parameter. Simulation results show that maximizing the network capacity and reducing the packet travel time can generate an optimal parameter value. Compared with the strategy of adopting exclusive local static information, the new strategy shows its advantages in improving the efficiency of the system. The detailed analysis of the mixing strategy is provided for explaining its effects on traffic routing. The work indicates that effectively utilizing the larger degree nodes plays a key role in scale-free traffic systems.

Epidemic spreading on heterogeneous networks with identical infectivity

In this Letter, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, A, at each time step. In contrast to the previous studies, we find that on scale-free networks, the density of the recovered individuals in the present model shows a threshold behavior. We obtain the analytical results using the mean-field theory and find that the threshold value equals 1/A, indicating that the threshold value is independent of the topology of the underlying network. The simulations agree well with the analytic results. Furthermore, we study the time behavior of the epidemic propagation and find a hierarchical dynamics with three plateaus. Once the highly connected hubs are reached, the infection pervades almost the whole network in a progressive cascade across smaller degree classes. Then, after the previously infected hubs are recovered, the disease can only propagate to the class of smallest degree till the infected individuals are all recovered. The present results could be of practical importance in the setup of dynamic control strategies.

Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing

An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.

Particle Swarm Optimization with Scale-Free Interactions

The particle swarm optimization (PSO) algorithm, in which individuals collaborate with their interacted neighbors like bird flocking to search for the optima, has been successfully applied in a wide range of fields pertaining to searching and convergence. Here we employ the scale-free network to represent the inter-individual interactions in the population, named SF-PSO. In contrast to the traditional PSO with fully-connected topology or regular topology, the scale-free topology used in SF-PSO incorporates the diversity of individuals in searching and information dissemination ability, leading to a quite different optimization process. Systematic results with respect to several standard test functions demonstrate that SF-PSO gives rise to a better balance between the convergence speed and the optimum quality, accounting for its much better performance than that of the traditional PSO algorithms. We further explore the dynamical searching process microscopically, finding that the cooperation of hub nodes and non-hub nodes play a crucial role in optimizing the convergence process. Our work may have implications in computational intelligence and complex networks.

Noise Bridges Dynamical Correlation and Topology in Coupled Oscillator Networks

We study the relationship between dynamical properties and interaction patterns in complex oscillator networks in the presence of noise. A striking finding is that noise leads to a general, one-to-one correspondence between the dynamical correlation and the connections among oscillators for a variety of node dynamics and network structures. The universal finding enables an accurate prediction of the full network topology based solely on measuring the dynamical correlation. The power of the method for network inference is demonstrated by the high success rate in identifying links for distinct dynamics on both model and real-life networks. The method can have potential applications in various fields due to its generality, high accuracy, and efficiency.

Efficient routing on scale-free networks based on local information

In this Letter, we propose a new routing strategy with a single tunable parameter α only based on local information of network topology. The probability that a given node i with degree ki receives packets from its neighbors is proportional to k α . In order to maximize the packets handling capacity of underlying structure that can be measured by the critical point of continuous phase transition from free flow to congestion, the optimal value of α is sought out. Through investigating the distributions of queue length on each node in free state, we give an explanation why the delivering capacity of the network can be enhanced by choosing the optimal α. Furthermore, dynamic properties right after the critical point are also studied. Interestingly, it is found that although the system enters the congestion state, it still possesses partial delivering capability whi ch does not depend on α. This phenomenon suggests that the capacity of the scale-free network can be enhanced by increasing the forwarding ability of small important nodes which bear severe congestion.  2005 Elsevier B.V. All rights reserved.

Collective synchronization induced by epidemic dynamics on complex networks with communities.

Much recent empirical evidence shows that community structure is ubiquitous in the real-world networks. In this paper we propose a growth model to create scale-free networks with the tunable strength (noted by Q ) of community structure and investigate the influence of community strength upon the collective synchronization induced by Susceptive-Infected-Recovery-Susceptive (SIRS) epidemiological process. Global and local synchronizability of the system is studied by means of an order parameter and the relevant finite-size scaling analysis is provided. The numerical results show that a phase transition occurs at Qc approximately or equal to 0.835 from global synchronization to desynchronization and the local synchronization is weakened in a range of intermediately large Q. Moreover, we study the impact of mean degree upon synchronization on scale-free networks.