Dynamic properties of chasers in a moving queue based on a delayed chasing model

A delayed chasing model is proposed to simulate the chase behavior in the queue, where each member regards the closest one ahead as the target, and the leader is attracted to a target point with slight fluctuation. When the initial distances between neighbors possess an identical low value, the fluctuating target of the leader can cause an amplified disturbance in the queue. After a long period of time, the queue recovers the stable state from the disturbance, forming a straightline-like pattern again, but distances between neighbors grow. Whether the queue can keep stable or not depends on initial distance, desired velocity, and relaxation time. Furthermore, we carry out convergence analysis to explain the divergence transformation behavior and confirm the convergence conditions, which is in approximate agreement with simulations.     

GeoGebra辅助平面向量的教学探究——以“平面向量基本定理及坐标表示”为例

通过GeoGebra软件,将原本抽象的数学概念和定理予以直观化、动态化,分别从几何和代数两方面来揭示数学对象的本质,从而加强学生对数学抽象概念和定理的透彻理解.以“平面向量基本定理及坐标表示”的教学为例,探究GeoGebra软件在辅助平面向量教学方面的应用.     

Traffic resource allocation for complex networks

In this paper, an optimal resource allocation strategy is proposed to enhance traffic dynamics in complex networks. The network resources are the total node packet-delivering capacity and the total link bandwidth. An analytical method is developed to estimate the overall network capacity by using the concept of efficient betweenness (ratio of algorithmic betweenness and local processing capacity). Three network structures (scale-free, small-world, and random networks) and two typical routing protocols (shortest path protocol and efficient routing protocol) are adopted to demonstrate the performance of the proposed strategy. Our results show that the network capacity is reversely proportional to the average path length for a particular routing protocol and the shortest path protocol can achieve the largest network capacity when the proposed resource allocation strategy is adopted.     

Synchronization in multilayer networks through different coupling mechanisms

In recent years, most studies of complex networks have focused on a single network and ignored the interaction of multiple networks, much less the coupling mechanisms between multiplex networks. In this paper we investigate synchronization phenomena in multilayer networks with nonidentical topological structures based on three specific coupling mechanisms:assortative, disassortative, and anti-assortative couplings. We find rich and complex synchronous dynamic phenomena in coupled networks. We also study the behavior of effective frequencies for layers I and II to understand the underlying microscopic dynamics occurring under the three different coupling mechanisms. In particular, the coupling mechanisms proposed here have strong robustness and effectiveness and can produce abundant synchronization phenomena in coupled networks.     

Effect of Mixing Assortativity on Extreme Events in Complex Networks

We investigate the effect of mixing assortativity on the occurrence of extreme events in complex networks. The bias random walk model is adopted with a preferential transition probability tuned by a parameter We derive exact expressions for the stationary distribution probability and for the occurrence probability of extreme events. They reveal that the occurrence of extreme events strongly depends on the mixing assortativity of the network. It is shown that, for non-assortative （rk = 0）, assortative （rk = 0.15） and disassortative （rk = -0.15） scale-free networks, the minimal occurrence of extreme events will happen at α= -1.0, α = -0.6 ands = 0.2, respectively.     

Evolutionary Prisoner's Dilemma Game Based on Pursuing Higher Average Payoff

We investigate the prisoner＇s dilemma game based on a new rule： players will change their current strategies to opposite strategies with some probability if their neighbours＇ average payoffs are higher than theirs. Compared with the cases on regular lattices （RL） and Newman-Watts small world network （NW）, cooperation can be best enhanced on the scale-free Barabasi-Albert network （BA）. It is found that cooperators are dispersive on RL network, which is different from previously reported results that cooperators will form large clusters to resist the invasion of defectors. Cooperative behaviours on the BA network are discussed in detail. It is found that large-degree individuals have lower cooperation level and gain higher average payoffs than that of small-degree individuals. In addition, we find that small-degree individuals more frequently change strategies than do large- degree individuals.     

基于GeoGebra的数学概念的教学探究——以“椭圆定义的多种形式”为例

GeoGebra软件能够将代数语言转化为几何语言,使原本抽象的数学概念可视化,加强学生对数学抽象概念的深入理解,有助于培养学生的数形结合能力.本文以“椭圆定义的多种形式”的可视化教学为例,探究GeoGebra软件在抽象的数学概念方面的教学应用.     

Effects of node buffer and capacity on network traffic

In this paper, we study the optimization of network traffic by considering the effects of node buffer ability and capacity. Two node buffer settings are considered. The node capacity is considered to be proportional to its buffer ability. The node effects on network traffic systems are studied with the shortest path protocol and an extension of the optimal routing [Phys. Rev. E 74 046106 (2006)]. In the diagrams of flux-density relationships, it is shown that a nodes buffer ability and capacity have profound effects on the network traffic.