Prisoner＇s Dilemma Game with Heterogeneous Influential Effect on Regular Small-World Networks

The effect of heterogeneous influence of different individuals on the maintenance of co-operative behaviour is studied in an evolutionary Prisoner＇s Dilemma game with players located on the sites of regular small-world networks. The players interacting with their neighbours can either co-operate or defect and update their states by choosing one of the neighbours and adopting its strategy with a probability depending on the pay off difference. The selection of the neighbour obeys a preferential rule： the more influential a neighbour, the larger the probability it is picked. It is found that this simple preferential selection rule can promote continuously the co-operation of the whole population with the strengthening of the disorder of the underlying network.     

Synchronization of Coupled Oscillators on Newman-Watts Small-World Networks

We investigate the collection behaviour of coupled phase oscillators on Newman-Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scaling. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.     

Rank-based deactivation model for networks with age

We study the impact of age on network evolution which couples addition of new nodes and deactivation of old ones. During evolution, each node experiences two stages: active and inactive. The transition from the active state to the inactive one is based on the rank of the node. In this paper, we adopt age as a criterion of ranking, and propose two deactivation models that generalize previous research. In model A, the older active node possesses the higher rank, whereas in model B, the younger active node takes the higher rank. We make a comparative study between the two models through the node-degree distribution.     

Time-varying networks based on activation and deactivation mechanisms

A class of models for activity-driven networks is proposed in which nodes vary in two states: active and inactive.Only active nodes can receive links from others which represent instantaneous dynamical interactions. The evolution of the network couples the addition of new nodes and state transitions of old ones. The active group changes with activated nodes entering and deactivated ones leaving. A general differential equation framework is developed to study the degree distribution of nodes of integrated networks where four different schemes are formulated.     

Phase Locking Phenomena and Electroencephalogram-Like Activities in Dynamic Neuronal Systems

We study signal detection and transduction of dynamic neuronal systems under the influence of external noise,white and coloured. Based on simulations, we show explicitly phase locking phenomena between the output and the input of a single neuron and Electroencephalogram-like activities on neural networks with small-world connectivity. The numerical results prove that the dynamic neuronal system can be adjusted to an optimal sensitive state for signal processing in the presence of additive noise.     

Generating weighted community networks based on local events

Many realistic networks have community structures, namely, a network consists of groups of nodes within which links are dense but among which links are sparse. This paper proposes a growing network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Also, it utilizes the preferential attachment for building connections determined by nodes' strengths, which evolves dynamically during the growth of the system. The resulting network reflects the intrinsic community structure with generalized power-law distributions of nodes' degrees and strengths.     

Evolution of Weighted Networks with Exponential Aging of Sites

We study the growth of weighted networks with exponential aging of sites. Each new vertex of the network is connected to some old vertices with proportional (i) to the strength of the old vertex and (ii) to e^-αT, where T is the age of the old vertex and α is a positive constant. As soon as the preferential attachment is modified by such factors, the interesting quantities of the produced network (the vertex degree, vertex strength, clustering coefficient and average path length) will be significantly transformed.     

Risk Estimate of Diseases in Scale-Free Networks

We investigate the effect of risk estimate on the spread of diseases by the standard susceptible-infected- susceptible （SIS） model. The perception of the risk of being infected is explained as cutting off links among individuals, either healthy or infected, We study this simple dynamics on scale-free networks by analytical methods and computer simulations. We obtain the self-consistency form for the infection prevalence in steady states. For a given transmission rate, there exists a linear relationship between the reciprocal of the density of infected nodes and the estimate parameter. We confirm all the results by sufficient numerical simulations.     

Walks on Weighted Networks

We investigate the dynamics of random walks on weighted networks. Assuming that the edge weight and the node strength are used as local information by a random walker. Two kinds of walks, weight-dependent walk and strength-dependent walk, are studied. Exact expressions for stationary distribution and average return time are derived and confirmed by computer simulations. The distribution of average return time and the mean-square displacement are calculated for two walks on the Barrat-Barthelemy-Vespignani （BBV） networks. It is found that a weight-dependent walker can arrive at a new territory more easily than a strength-dependent one.     

Improving consensual performance of multi-agent systems in weighted scale-free networks

This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is determined by the relative degree of the involved nodes. It shows that the asymmetry of interactions has a great effect on the consensus. Especially, when the interactions are dominant from higher- to lower-degree nodes, both the convergence speed and the robustness to communication delay are enhanced.