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...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.展开更多
我们在常规小世界的网络上与非线性的吸引人的效果调查一个空间囚犯的窘境比赛。位于网络的地点的播放器也能与他们的邻居或缺点一起合作。在每代，每个播放器由第一与与 A 成正比的可能性选择邻居之一更新它的策略(高山哈) 表示邻居的...我们在常规小世界的网络上与非线性的吸引人的效果调查一个空间囚犯的窘境比赛。位于网络的地点的播放器也能与他们的邻居或缺点一起合作。在每代，每个播放器由第一与与 A 成正比的可能性选择邻居之一更新它的策略(高山哈) 表示邻居的优美， A 在此收集了发薪并且一(】= 0 ) 是描绘非线性的效果的程度的一个免费参数。然后，每个播放器在他们的发薪差别上与一个概率依赖者采用它的策略。用蒙特卡罗模拟，我们为高山的各种各样的值处于静止状态调查合作者的密度 PC 哈并且网络的给换新电线的概率 q。如此的吸引人的效果的介绍显著地支持合作的出现和坚持在上，这被显示出大量为一样的网络背叛的诱惑组织。我们也指出远程的连接任何一个提高或禁止合作，它取决于高山的价值哈并且发薪参数 b。展开更多
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 weight...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).展开更多
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 ...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.展开更多
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 autocorr...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.展开更多
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 ran...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.展开更多
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^-αT, wh...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^-αT, where T 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.展开更多
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 siz...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 m, 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 m 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.展开更多
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 W...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 Barabá si-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/ν,γ/ν and 1/ν 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.展开更多
文摘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.
文摘我们在常规小世界的网络上与非线性的吸引人的效果调查一个空间囚犯的窘境比赛。位于网络的地点的播放器也能与他们的邻居或缺点一起合作。在每代，每个播放器由第一与与 A 成正比的可能性选择邻居之一更新它的策略(高山哈) 表示邻居的优美， A 在此收集了发薪并且一(】= 0 ) 是描绘非线性的效果的程度的一个免费参数。然后，每个播放器在他们的发薪差别上与一个概率依赖者采用它的策略。用蒙特卡罗模拟，我们为高山的各种各样的值处于静止状态调查合作者的密度 PC 哈并且网络的给换新电线的概率 q。如此的吸引人的效果的介绍显著地支持合作的出现和坚持在上，这被显示出大量为一样的网络背叛的诱惑组织。我们也指出远程的连接任何一个提高或禁止合作，它取决于高山的价值哈并且发薪参数 b。
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575072 and 11475074)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2017-172)
文摘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).
基金supported by the National Natural Science Foundation of China (Grant No. 10775060)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575072 and 11675096)the Fundamental Research Funds for the Central Universities,China(Grant No.GK201702001)the FPALAB-SNNU,China(Grant No.16QNGG007)
文摘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.
文摘我们学习发生在一枚常规戒指上的一个基于记忆的布尔游戏(MBBG ) ，每个代理人在那里根据它最后 M 时间步骤的本地最佳的状态行动，在存储器记录了，并且在少数的代理人被奖励。在 0 和 1 之间的一免费 perameter p 被介绍表示力量 p， MBBG 系统能自发地比随机的游戏更好演变到性能的一个状态；当时为更大的 p ，牧群行为出现减少系统利润由在记忆能力 M 上分析系统的动力学的 dependance ，我们发现一个更高的记忆能力赞成更好的表演状态的出现，并且有效地制止牧群行为，因此增加系统利润。就长期的记忆的高费用而言，为制止牧群行为的记忆能力的改进也被讨论，并且 M = 5 被建议是一种好选择。
基金supported by the National Natural Science Foundation of China (Grant Nos. 60870013 and 10832006)
文摘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.
文摘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^-αT, where T 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.
基金Project supported by the National Natural Science Foundation of China (Grant No 10775060)
文摘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 m, 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 m 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.
基金Project supported by the National Natural Science Foundation of China (Grant No.10775060)
文摘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 Barabá si-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/ν,γ/ν and 1/ν 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.
