We propose a packet routing strategy with a tunable parameter based on the local structural information of a scale-free network. As free traffic flow on the communication networks is key to their normal and efficient functioning, we focus on the network capacity that can be measured by the critical point of phase transition from free flow to congestion. Simulations show that the maximal capacity corresponds to alpha= -1 in the case of identical nodes' delivering ability. To explain this, we investigate the number of packets of each node depending on its degree in the free flow state and observe the power law behavior. Other dynamic properties including average packets traveling time and traffic load are also studied. Inspiringly, our results indicate that some fundamental relationships exist between the dynamics of synchronization and traffic on the scale-free networks.

Despite the long history of modelling human mobility, we continue to lack a highly accurate approach with low data requirements for predicting mobility patterns in cities. Here, we present a population-weighted opportunities model without any adjustable parameters to capture the underlying driving force accounting for human mobility patterns at the city scale. We use various mobility data collected from a number of cities with different characteristics to demonstrate the predictive power of our model. We find that insofar as the spatial distribution of population is available, our model offers universal prediction of mobility patterns in good agreement with real observations, including distance distribution, destination travel constraints and flux. By contrast, the models that succeed in modelling mobility patterns in countries are not applicable in cities, which suggests that there is a diversity of human mobility at different spatial scales. Our model has potential applications in many fields relevant to mobility behaviour in cities, without relying on previous mobility measurements.

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 4 and 8-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.