Newman-Watts Small-world Networks Research Articles

Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network

We focus on the heterogeneity of social networks and its role to the emergence of prevailing cooperators and sustainable cooperation. The social networks are representative of the interaction relationships between players and their encounters in each round of games. We study an evolutionary Prisoner's Dilemma game on a variant of Newman-Watts small-world network, whose heterogeneity can be tuned by a parameter. It is found that optimal cooperation level exists at some intermediate topological heterogeneity for different temptations to defect. That is, frequency of cooperators peaks at a certain specific value of degree heterogeneity — neither the most heterogeneous case nor the most homogeneous one would favor the cooperators. Besides, the average degree of networks and the adopted update rule also affect the cooperation level.

Synchronization of Coupled Oscillators on Newman–WattsSmall-World Networks

We investigate the collection behaviour of coupled phase oscillatorson Newman–Watts small-world networks in one and two dimensions.Each component of the network is assumed as an oscillator andeach interacts with the others following the Kuramoto model. Wethen study the onset of global synchronization of phases andfrequencies based on dynamic simulations and finite-size scaling.Both the phase and frequency synchronization are observed toemerge in the presence of a tiny fraction of shortcuts andenhanced with the increases of nearest neighbours and latticedimensions.

Traversal times for random walks on small-world networks

We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate that is different from the rate for steps across small-world connections. When f>>F, the mean time to traverse the network exhibits a transition associated with percolation of the random graph (i.e., small-world) part of the network, and a collapse of the data onto a universal curve. This transition was not observed in earlier studies in which equal transition rates were assumed for all allowed steps. We develop a simple self-consistent effective-medium theory and show that it gives a quantitatively correct description of the traversal time in all parameter regimes except the immediate neighborhood of the transition, as is characteristic of most effective-medium theories.

Spatial prisoner’s dilemma game with volunteering in Newman-Watts small-world networks

A modified spatial prisoner's dilemma game with voluntary participation in Newman-Watts small-world networks is studied. Some reasonable ingredients are introduced to the game evolutionary dynamics: each agent in the network is a pure strategist and can only take one of three strategies (cooperator, defector, and loner); its strategical transformation is associated with both the number of strategical states and the magnitude of average profits, which are adopted and acquired by its coplayers in the previous round of play; a stochastic strategy mutation is applied when it gets into the trouble of local commons that the agent and its neighbors are in the same state and get the same average payoffs. In the case of very low temptation to defect, it is found that agents are willing to participate in the game in typical small-world region and intensive collective oscillations arise in more random region.