具有层级结构集体影响力的多数投票模型

多数投票模型是观点动力学研究中的常用模型,本文在多数投票模型的基础上引入了具有层级结构的集体影响力,以节点周边层级结构上的节点的度衡量中心节点的观点权重,即为集体影响力参数.通过蒙特卡罗模拟,研究了具有集体影响力的多数投票模型在ER(Erdos and Rényi)随机网络与无标度网络上观点的演化,发现系统观点均出现了有序-无序相变,且相比原始多数投票模型更容易趋于无序,即相变临界点更小.原因是考虑具有层级结构的集体影响力时,系统的集体影响力参数值整体减小,且分布数目随着参数值的增大而减少,呈“长尾”趋势,占少数的高影响力个体使周围节点的观点产生跟随现象,随着噪声参数的增大,当少数的高影响力个体趋于无序时,整个系统也会趋于无序,即系统更容易达到无序状态.最后通过有限尺寸标度法,发现无论在ER随机网络或在无标度网络中,具有集体影响力的多数投票模型的相变均为Ising模型普适类.

Non-monotonic behavior of jam probability and stretchedexponential distribution in pedestrian counterflow

We adopt a floor field cellular automata model to study the statistical properties of bidirectional pedestrian flow movingin a straight corridor. We introduce a game-theoretic framework to deal with the conflict of multiple pedestrians tryingto move to the same target location. By means of computer simulations, we show that the complementary cumulative distributionof the time interval between two consecutive pedestrians leaving the corridor can be fitted by a stretched exponentialdistribution, and surprisingly, the statistical properties of the two types of pedestrian flows are affected differently by theflow ratio, i.e., the ratio of the pedestrians walking toward different directions. We also find that the jam probability exhibitsa non-monotonic behavior with the flow ratio, where the worst performance arises at an intermediate flow ratio of around0.2. Our simulation results are consistent with some empirical observations, which suggest that the peculiar characteristicsof the pedestrians may attributed to the anticipation mechanism of collision avoidance.

复杂网络上的博弈

博弈理论在社会、经济、生物以及生态等系统中存在着广泛的应用,复杂网络理论则是研究复杂系统全新而有力的工具,因此将博弈理论与复杂网络理论相结合成为研究复杂系统一个新的热点.概述国内外当前关于复杂网络上博弈动力学的研究情况和发展动态,包括基本的博弈模型、主要关注的问题、以及网络结构和博弈动力学的相互作用等,最后探讨进一步的研究课题.

复杂网络2012年度盘点

复杂网络是复杂性科学研究中受到最广泛关注的方向，在信息科学、物理学、生物学、数学乃至社会学、管理学等领域都产生了重大贡献和持续影响。十几年来，复杂网络的研究成果一直是《自然》、《科学》、《美国科学院院刊》等综合类顶级学术期刊的宠儿，每年均有数10篇相关论文发表。

共演博弈下网络合作动力学研究进展

综述了网络上共演博弈最近的研究进展,首先基于囚徒困境和公共品博弈模型,系统比较了无标度网络上度异质性、度相关性和聚类特性对于两人和多人博弈作用机理的异同。然后,在静态网络上综述了近年从时间尺度、个体选择、教育活动、个体理性与期望、交互限制等方面提出的演化规则与合作行为共演的成果。进一步,从移边、生灭、基于格子和平面移动四方面,介绍了结构与合作行为协同演化的工作。最后探讨了今后值得研究的课题。

含时线性势Gross-Piteavskii方程的孤立波解

首先对双曲函数法进行了扩展,使其可用于求解变系数非线性演化方程,然后用此方法成功得到了Gross-Pitaevskii方程在某含时线性势下的两类精确解.结果表明在吸引势情形下,方程存在钟形包络孤立波解;在排斥势情形下,存在扭结形包络孤立波解.该方程可用来描述重力场中在随时间变化的外磁场作用下的玻色—爱因斯坦凝聚体的演化过程,故所得解具有重要的物理意义.

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.

Prisoner＇s Dilemma Game with Nonlinear Attractive Effect on Regular Small-World Networks

We investigate a spatial Prisoner＇s Dilemma game with nonlinear attractive effect on regular small-world networks. The players located on the sites of networks can either cooperate with their neighbours or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbours with a probability proportional to .A^α denoting the attractiveness of the neighbour, where .4 is the collected payoff and ^α （-〉0） is a free parameter characterizing the extent of nonlinear effect. Then each player adopts its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density pc of cooperators in the stationary state for various values of α and the rewiring probability q of the network. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect for the same network structures. We also point out that long-range connections either enhance or inhibit the cooperation, which depends on the value of α and the payoff parameter b.

Effects of the planarity and heterogeneity of networks on evolutionary two-player games

We study the effects of the planarity and heterogeneity of networks on evolutionary two-player symmetric games by considering four different kinds of networks, including two types of heterogeneous networks: the weighted planar stochastic lattice(a planar scale-free network) and the random uncorrelated scale-free network with the same degree distribution as the weighted planar stochastic lattice; and two types of homogeneous networks: the hexagonal lattice and the random regular network with the same degree k_0= 6 as the hexagonal lattice. Using extensive computer simulations, we found that both the planarity and heterogeneity of the network have a significant influence on the evolution of cooperation, either promotion or inhibition, depending not only on the specific kind of game(the Harmony, Snowdrift, Stag Hunt or Prisoner's Dilemma games), but also on the update rule(the Fermi, replicator or unconditional imitation rules).

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.

Memory-Based Boolean Game and Self-Organized Phenomena on Networks

We study a memory-based Boolean game （MBBG） taking place on a regular ring, wherein each agent acts according to its local optimal states of the last M time steps recorded in memory, and the agents in the minority are rewarded. One free parameter p between 0 and 1 is introduced to denote the strength of the agent willing to make a decision according to its memory. It is found that giving proper willing strength p, the MBBG system can spontaneously evolve to a state of performance better than the random game; while for larger p, the herd behaviour emerges to reduce the system profit. By analysing the dependence of dynamics of the system on the memory capacity M, we find that a higher memory capacity favours the emergence of the better performance state, and effectively restrains the herd behaviour, thus increases the system profit. Considering the high cost of long-time memory, the enhancement of memory capacity for restraining the herd behaviour is also discussed, and M =5 is suggested to be a good choice.

Quasi-periodic events on structured earthquake models

There has been much interest in studying quasi-periodic events on earthquake models.Here we investigate quasiperiodic events in the avalanche time series on structured earthquake models by the analysis of the autocorrelation function and the fast Fourier transform.For random spatial earthquake models, quasi-periodic events are robust and we obtain a simple rule for a period that is proportional to the choice of unit time and the dissipation of the system.Moreover, computer simulations validate this rule for two-dimensional lattice models and cycle graphs, but our simulation results also show that small-world models, scale-free models, and random rule graphs do not have periodic phenomena.Although the periodicity of avalanche does not depend on the criticality of the system or the average degree of the system or the size of the system,there is evidence that it depends on the time series of the average force of the system.

Evolutionary snowdrift game with disordered environments in mobile societies

We investigate an evolutionary snowdrift game on a square N ： L × L lattice with periodic boundary conditions, where a population of no （no ≤ N） players located on the sites of this lattice can either cooperate with or defect from their nearest neighbours. After each generation, every player moves with a certain probability p to one of the player＇s nearest empty sites. It is shown that, when p = 0, the cooperative behaviour can be enhanced in disordered structures. When p 〉 0, the effect of mobility on cooperation remarkably depends on the payoff parameter r and the density of individuals ρ （ρ = no/N）. Compared with the results of p = 0, for small r, the persistence of cooperation is enhanced at not too small values of p; whereas for large r, the introduction of mobility inhibits the emergence of cooperation at any p 〈 1; for the intermediate value of r, the cooperative behaviour is sometimes enhanced and sometimes inhibited, depending on the values of p and p. In particular, the cooperator density can reach its maximum when the values of p and p reach their respective optimal values. In addition, two absorbing states of all cooperators and all defectors can emerge respectively for small and large r in the case of p 〉 0.

Undetermination of the relation between network synchronizability and betweenness centrality

Betweenness centrality is taken as a sensible indicator of the synchronizability of complex networks. To test whether betweenness centrality is a proper measure of the synchronizability in specific realizations of random networks, this paper adds edges to the networks and then evaluates the changes of betweenness centrality and network synchronizability. It finds that the two quantities vary independently.

Cooperation influenced by the correlation degree of two-layered complex networks in evolutionary prisoner’s dilemma games

An evolutionary prisoner＇s dilemma game is investigated on two-layered complex networks respectively representing interaction and learning networks in one and two dimensions. A parameter q is introduced to denote the correlation degree between the two-layered networks. Using Monte Carlo simulations we studied the effects of the correlation degree on cooperative behaviour and found that the cooperator density nontrivially changes with q for different payoff parameter values depending on the detailed strategy updating and network dimension. An explanation for the obtained results is provided.

Synchronization of coupled logistic maps on random community networks

The collective synchronization of a system of coupled logistic maps on random community networks is investigated. It is found that the synchronizability of the community network is affected by two factors when the size of the network and the number of connections are fixed. One is the number of communities denoted by the parameter rn, and the other is the ratio σ of the connection probability p of each pair of nodes within each community to the connection probability q of each pair of nodes among different communities. Theoretical analysis and numerical results indicate that larger rn and smaller σ are the key to the enhancement of network synchronizability. We also testify synchronous properties of the system by analysing the largest Lyapunov exponents of the system.

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.

Effects of average degree of network on an order-disorder transition in opinion dynamics

We have investigated the influence of the average degree （k） of network on the location of an order-disorder transition in opinion dynamics. For this purpose, a variant of majority rule （VMR） model is applied to Watts-Strogatz （WS） small-world networks and Barabasi-Albert （BA） scale-free networks which may describe some non-trivial properties of social systems. Using Monte Carlo simulations, we find that the order-disorder transition point of the VMR model is greatly affected by the average degree （k） of the networks; a larger value of （k） results in a more ordered state of the system. Comparing WS networks with BA networks, we find WS networks have better orderliness than BA networks when the average degree （k） is small. With the increase of （k）, BA networks have a more ordered state. By implementing finite-size scaling analysis, we also obtain critical exponents β/v, γ/u and 1/v for several values of average degree （k）. Our results may be helpful to understand structural effects on order-disorder phase transition in the context of the majority rule model.

同伦分析法在求解非线性演化方程中的应用

利用同伦分析法求解了(2+1)维改进的Zakharov-Kuznetsov方程,得到了它的近似周期解,该解与精确解符合很好.结果表明,同伦分析法在求解高维非线性演化方程时,仍然是一种行之有效的方法.同时,还对该方法进行了一定的扩展,经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解.