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.     

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.     

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.     

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.