Search

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.

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.

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 payoff 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.

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−ατ, where τ 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.

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.