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1.
针对真实世界中大规模网络都具有明显聚类效应的特点, 提出一类具有高聚类系数的加权无标度网络演化模型, 该模型同时考虑了优先连接、三角结构、随机连接和社团结构等四种演化机制. 在模型演化规则中, 以概率p增加单个节点, 以概率1–p增加一个社团. 与以往研究的不同在于新边的建立, 以概率φ在旧节点之间进行三角连接, 以概率1–φ进行随机连接. 仿真分析表明, 所提出的网络度、强度和权值分布都是服从幂律分布的形式, 且具有高聚类系数的特性, 聚类系数的提高与社团结构和随机连接机制有直接的关系. 最后通过数值仿真分析了网络演化机制对同步动态特性的影响, 数值仿真结果表明, 网络的平均聚类系数越小, 网络的同步能力越强.
关键词:
无标度网络
加权网络
聚类系数
同步能力 相似文献
2.
Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks. 相似文献
3.
M. Zhao T. Zhou B.-H. Wang Q. Ou J. Ren 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(3):375-379
In this paper, inspired by the idea that different nodes should
play different roles in network synchronization, we bring forward
a coupling method where the coupling strength of each node depends
on its neighbors' degrees. Compared with the uniform coupled
method and the recently proposed Motter-Zhou-Kurths method, the
synchronizability of scale-free networks can be remarkably
enhanced by using the present coupling method, and the highest
network synchronizability is achieved at β=1 which is
similar to a method introduced in [AIP Conf. Proc. 776, 201
(2005)]. 相似文献
4.
Enhancing the network synchronizability 总被引:1,自引:0,他引:1
The structural and dynamical properties, particularly the small-world effect and scale-free feature, of complex networks have
attracted tremendous interest and attention in recent years. This article offers a brief review of one focal issue concerning
the structural and dynamical behaviors of complex network synchronization. In the presentation, the notions of synchronization
of dynamical systems on networks, stability of dynamical networks, and relationships between network structure and synchronizability,
will be first introduced. Then, various technical methods for enhancing the network synchronizability will be discussed, which
are roughly divided into two classes: Structural Modification and Coupling-Pattern Regulation, where the former includes three
typical methods—dividing hub nodes, shortening average distances, and deleting overload edges, while the latter mainly is
a method of strengthening the hub-nodes’ influence on the network.
相似文献
5.
Z.-Z. Zhang S.-G. Zhou T. Zou 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(3):259-271
In this paper, firstly, we study analytically the topological
features of a family of hierarchical lattices (HLs) from the view
point of complex networks. We derive some basic properties of HLs
controlled by a parameter q: scale-free degree distribution with
exponent γ=2+ln 2/(ln q), null clustering
coefficient, power-law behavior of grid coefficient, exponential
growth of average path length (non-small-world), fractal scaling
with dimension dB=ln (2q)/(ln 2), and disassortativity.
Our results show that scale-free networks are not always
small-world, and support the conjecture that self-similar scale-free
networks are not assortative. Secondly, we define a deterministic
family of graphs called small-world hierarchical lattices (SWHLs).
Our construction preserves the structure of hierarchical lattices,
including its degree distribution, fractal architecture, clustering
coefficient, while the small-world phenomenon arises. Finally, the
dynamical processes of intentional attacks and collective
synchronization are studied and the comparisons between HLs and
Barabási-Albert (BA) networks as well as SWHLs are shown. We
find that the self-similar property of HLs and SWHLs significantly
increases the robustness of such networks against targeted damage on
hubs, as compared to the very vulnerable non fractal BA networks,
and that HLs have poorer synchronizability than their counterparts
SWHLs and BA networks. We show that degree distribution of
scale-free networks does not suffice to characterize their
synchronizability, and that networks with smaller average path
length are not always easier to synchronize. 相似文献
6.
Y. Huang L. Wu S. Q. Zhu 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,69(3):431-438
The interaction between the evolution of the game and the underlying network structure with evolving snowdrift game model
is investigated. The constructed network follows a power-law degree distribution typically showing scale-free feature. The
topological features of average path length, clustering coefficient, degree-degree correlations and the dynamical feature
of synchronizability are studied. The synchronizability of the constructed networks changes by the interaction. It will converge
to a certain value when sufficient new nodes are added. It is found
that initial payoffs of nodes greatly affect the synchronizability. When initial payoffs for players are equal, low common
initial payoffs may lead to more heterogeneity of the network and good
synchronizability. When initial payoffs follow certain distributions, better synchronizability is obtained compared to equal
initial payoff. The result is also true for phase synchronization of nonidentical oscillators. 相似文献
7.
Synchronization in different types of weighted networks based on a scale-free weighted network model is investigated. It has been argued that heterogeneity suppresses synchronization in unweighted networks [T. Nishikawa, A.E. Motter, Y.C. Lai, F.C. Hoppensteadt, Phys. Rev. Lett. 91 (2003) 014101]. However, it is shown in this work that as the network becomes more heterogeneous, the synchronizability of Type I symmetrically weighted networks, and Type I and Type II asymmetrically weighted networks is enhanced, while the synchronizability of Type II symmetrically weighted networks is weakened. 相似文献
8.
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. 相似文献
9.
10.
M. Ponce C. C. Masoller Arturo C. Martí 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(1):83-93
We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local
dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two regimes
of synchronization, depending on the distribution of delays: when the delays are sufficiently heterogeneous the network synchronizes
on a steady-state (that is unstable for the uncoupled maps); when the delays are homogeneous, it synchronizes in a time-dependent
state (that is either periodic or chaotic). Using two global indicators we quantify the synchronizability on the two regimes,
focusing on the roles of the network connectivity and the topology. The connectivity is measured in terms of the average number
of links per node, and we consider various topologies (scale-free, small-world, star, and nearest-neighbor with and without
a central hub). With weak connectivity and weak coupling strength, the network displays an irregular oscillatory dynamics
that is largely independent of the topology and of the delay distribution. With heterogeneous delays, we find a threshold
connectivity level below which the network does not synchronize, regardless of the network size. This minimum average number
of neighbors seems to be independent of the delay distribution. We also analyze the effect of self-feedback loops and find
that they have an impact on the synchronizability of small networks with large coupling strengths. The influence of feedback,
enhancing or degrading synchronization, depends on the topology and on the distribution of delays. 相似文献
11.
We study synchronization transitions and pattern formation on small-world networks consisting of Morris-Lecar excitable neurons in dependence on the information transmission delay and the rewiring probability. In addition, networks formed via gap junctional connections and coupling via chemical synapses are considered separately. For gap-junctionally coupled networks we show that short delays can induce zigzag fronts of excitations, whereas long delays can further detriment synchronization due to a dynamic clustering anti-phase synchronization transition. For the synaptically coupled networks, on the other hand, we find that the clustering anti-phase synchronization can appear as a direct consequence of the prolongation of information transmission delay, without being accompanied by zigzag excitatory fronts. Irrespective of the coupling type, however, we show that an appropriate small-world topology can always restore synchronized activity if only the information transmission delays are short or moderate at most. Long information transmission delays always evoke anti-phase synchronization and clustering, in which case the fine-tuning of the network topology fails to restore the synchronization of neuronal activity. 相似文献
12.
多层网络是当今网络科学研究的一个前沿方向.本文深入研究了两层星形网络的特征值谱及其同步能力的问题.通过严格导出的两层星形网络特征值的解析表达式,分析了网络的同步能力与节点数、层间耦合强度和层内耦合强度的关系.当同步域无界时,网络的同步能力只与叶子节点之间的层间耦合强度和网络的层内耦合强度有关;当叶子节点之间的层间耦合强度比较弱时,同步能力仅依赖于叶子节点之间的层间耦合强度;而当层内耦合强度比较弱时,同步能力依赖于层内耦合强度;当同步域有界时,节点数、层间耦合强度和层内耦合强度对网络的同步能力都有影响.当叶子节点之间的层间耦合强度比较弱时,增大叶子节点之间的层间耦合强度会增强网络的同步能力,而节点数、中心节点之间的层间耦合强度和层内耦合强度的增大反而会减弱网络的同步能力;而当层内耦合强度比较弱时,增大层内耦合强度会增强网络的同步能力,而节点数、层间耦合强度的增大会减弱网络的同步能力.进一步,在层间和层内耦合强度都相同的基础上,讨论了如何改变耦合强度更有利于同步.最后,对两层BA无标度网络进行数值仿真,得到了与两层星形网络非常类似的结论. 相似文献
13.
W. L. Lu F. M. Atay J. Jost 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(3):399-406
Complexity of dynamical networks can arise not only from
the complexity of the topological structure but also from the time
evolution of the topology. In this paper, we study the synchronous
motion of coupled maps in time-varying complex networks both
analytically and numerically. The temporal variation is rather
general and formalized as being driven by a metric dynamical system.
Four network models are discussed in detail in which the
interconnections between vertices vary through time randomly. These
models are: 1) i.i.d. sequences of random graphs with fixed wiring
probability, 2) groups of graphs with random switches between the
individual graphs, 3) graphs with temporary random failures of
nodes, and 4) the meet-for-dinner model where the vertices are
randomly grouped. We show that the temporal variation and randomness
of the connection topology can enhance synchronizability in many
cases; however, there are also instances where they reduce
synchronizability. In analytical terms, the Hajnal diameter of the
coupling matrix sequence is presented as a measure for the
synchronizability of the graph topology. In topological terms, the
decisive criterion for synchronization of coupled chaotic maps is
that the union of the time-varying graphs contains a spanning tree. 相似文献
14.
Synchronizability of complex oscillators networks has attracted much
research interest in recent years. In contrast, in this paper we
investigate numerically the synchronization speed, rather than the
synchronizability or synchronization stability, of identical
oscillators on complex networks with communities. A new weighted
community network model is employed here, in which the community
strength could be tunable by one parameter δ. The results
showed that the synchronization speed of identical oscillators on
community networks could reach a maximal value when δ is
around 0.1. We argue that this is induced by the competition
between the community partition and the scale-free property of the
networks. Moreover, we have given the corresponding analysis through
the second least eigenvalue λ2 of the Laplacian matrix of
the network which supports the previous result that the
synchronization speed is determined by the value of λ2. 相似文献
15.
Huang Liang Lai Ying-Cheng Kwangho Park Wang Xingang Lai Choy Heng Robert A. Gatenby 《Frontiers of Physics in China》2007,2(4):446-459
Synchronization in complex networks has been an active area of research in recent years. While much effort has been devoted
to networks with the small-world and scale-free topology, structurally they are often assumed to have a single, densely connected
component. Recently it has also become apparent that many networks in social, biological, and technological systems are clustered,
as characterized by a number (or a hierarchy) of sparsely linked clusters, each with dense and complex internal connections.
Synchronization is fundamental to the dynamics and functions of complex clustered networks, but this problem has just begun
to be addressed. This paper reviews some progress in this direction by focusing on the interplay between the clustered topology
and network synchronizability. In particular, there are two parameters characterizing a clustered network: the intra-cluster
and the inter-cluster link density. Our goal is to clarify the roles of these parameters in shaping network synchronizability.
By using theoretical analysis and direct numerical simulations of oscillator networks, it is demonstrated that clustered networks
with random inter-cluster links are more synchronizable, and synchronization can be optimized when inter-cluster and intra-cluster
links match. The latter result has one counterintuitive implication: more links, if placed improperly, can actually lead to
destruction of synchronization, even though such links tend to decrease the average network distance. It is hoped that this
review will help attract attention to the fundamental problem of clustered structures/synchronization in network science.
相似文献
16.
This paper investigates generalized synchronization of three typical classes of complex dynamical networks: scale-free networks, small-world networks, and interpolating networks. The proposed synchronization strategy is to adjust adaptively a node’s coupling strength based on the node’s local generalized synchronization information. By taking the auxiliary-system approach and using the Lyapunov function method, we prove that for any given initial coupling strengths, the generalized synchronization can take place in complex networks consisting of nonidentical dynamical systems. It is demonstrated that the coupling strengths are affected by topologies of the networks. Furthermore, it is found that there are hierarchical features in the processes of generalized synchronization in scale-free networks because of their highly heterogeneous distributions of connection degree. Finally, we discuss in detail how a network’s degree of heterogeneity affects its generalization synchronization behavior. 相似文献
17.
In this paper, we present an algorithm for enhancing synchronizability of dynamical networks with prescribed degree distribution. The algorithm takes an unweighted and undirected network as input and outputs a network with the same node-degree distribution and enhanced synchronization properties. The rewirings are based on the properties of the Laplacian of the connection graph, i.e., the eigenvectors corresponding to the second smallest and the largest eigenvalues of the Laplacian. A term proportional to the eigenvectors is adopted to choose potential edges for rewiring, provided that the node-degree distribution is preserved. The algorithm can be implemented on networks of any sizes as long as their eigenvalues and eigenvectors can be calculated with standard algorithms. The effectiveness of the proposed algorithm in enhancing the network synchronizability is revealed by numerical simulation on a number of sample networks including scale-free, Watts-Strogatz, and Erdo?s-Re?nyi graphs. Furthermore, a number of network's structural parameters such as node betweenness centrality, edge betweenness centrality, average path length, clustering coefficient, and degree assortativity are tracked as a function of optimization steps. 相似文献
18.
A maximum entropy (ME) method to generate typical scale-free networks has been recently introduced. We investigate the controllability of ME networks and Barabási–Albert preferential attachment networks. Our experimental results show that ME networks are significantly more easily controlled than BA networks of the same size and the same degree distribution. Moreover, the control profiles are used to provide insight into control properties of both classes of network. We identify and classify the driver nodes and analyze the connectivity of their neighbors. We find that driver nodes in ME networks have fewer mutual neighbors and that their neighbors have lower average degree. We conclude that the properties of the neighbors of driver node sensitively affect the network controllability. Hence, subtle and important structural differences exist between BA networks and typical scale-free networks of the same degree distribution. 相似文献
19.
We study the synchronization of coupled phase oscillators in random complex networks. The topology of the networks is assumed to be vary over time. Here we mainly study the onset of global phase synchronization when the topology switches rapidly over time. We find that the results are, to some extent, different from those in deterministic situations. In particular, the synchronizability of coupled oscillators can be enhanced in ER networks and scale-free networks under fast switching, while in stochastic small-world networks such enhancement is not significant. 相似文献
20.
In this paper, we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p. The model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned. With the increase in the local information, the degree correlation of the network transforms from assortative to disassortative. We also study the distribution of the degree, strength and edge weight, which all show crossover between exponential and scale-free. Finally, an application of the proposed model to the study of the synchronization is considered. It is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced. 相似文献