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1.
It has been shown that synchronizability of a network is determined by the local structure rather than the global properties. With the same global properties, networks may have very different synchronizability. In this paper, we numerically studied, through the spectral properties, the synchronizability of ensembles of networks with prescribed statistical properties. Given a degree sequence, it is found that the eigenvalues and eigenratios characterizing network synchronizability have well-defined distributions, and statistically, the networks with extremely poor synchronizability are rare. Moreover, we compared the synchronizability of three network ensembles that have the same nodes and average degree. Our work reveals that the synchronizability of a network can be significantly affected by the local pattern of connections, and the homogeneity of degree can greatly enhance network synchronizability for networks of a random nature. 相似文献
2.
Synchronization in complex networks with a modular structure 总被引:1,自引:0,他引:1
Networks with a community (or modular) structure arise in social and biological sciences. In such a network individuals tend to form local communities, each having dense internal connections. The linkage among the communities is, however, much more sparse. The dynamics on modular networks, for instance synchronization, may be of great social or biological interest. (Here by synchronization we mean some synchronous behavior among the nodes in the network, not, for example, partially synchronous behavior in the network or the synchronizability of the network with some external dynamics.) By using a recent theoretical framework, the master-stability approach originally introduced by Pecora and Carroll in the context of synchronization in coupled nonlinear oscillators, we address synchronization in complex modular networks. We use a prototype model and develop scaling relations for the network synchronizability with respect to variations of some key network structural parameters. Our results indicate that random, long-range links among distant modules is the key to synchronization. As an application we suggest a viable strategy to achieve synchronous behavior in social networks. 相似文献
3.
In this paper, we propose a simple model that can generate
small-world network with community structure. The network is
introduced as a tunable community organization with parameter r,
which is directly measured by the ratio of inter- to intra-community
connectivity, and a smaller r corresponds to a stronger community
structure. The structure properties, including the degree
distribution, clustering, the communication efficiency and
modularity are also analysed for the network. In addition, by using
the Kuramoto model, we investigated the phase synchronization on
this network, and found that increasing the fuzziness of community
structure will markedly enhance the network synchronizability;
however, in an abnormal region (r ≤ 0.001), the network has even
worse synchronizability than the case of isolated communities (r =
0). Furthermore, this network exhibits a remarkable
synchronization behaviour in topological scales: the oscillators of
high densely interconnected communities synchronize more easily, and
more rapidly than the whole network. 相似文献
4.
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
5.
W. L. Lu B. Liu T. Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,77(2):257-264
In this paper, we study cluster synchronization in general
bi-directed networks of nonidentical clusters, where all nodes in
the same cluster share an identical map. Based on the transverse
stability analysis, we present sufficient conditions for local
cluster synchronization of networks. The conditions are
composed of two factors: the common inter-cluster coupling, which
ensures the existence of an invariant cluster synchronization
manifold, and communication between each pair of nodes in the same
cluster, which is necessary for chaos synchronization. Consequently, we propose a
quantity to measure the cluster synchronizability for a network with
respect to the given clusters via a function of the eigenvalues
of the Laplacian corresponding to the generalized eigenspace
transverse to the cluster synchronization manifold. Then, we discuss
the clustering synchronous dynamics and cluster synchronizability
for four artificial network models: (i) p-nearest-neighborhood graph; (ii)
random clustering graph; (iii) bipartite random graph; (iv)
degree-preferred growing clustering network. From these network models, we are to
reveal how the intra-cluster and inter-cluster links affect the cluster
synchronizability. By numerical examples, we find that for the first
model, the cluster synchronizability regularly enhances with the
increase of p, yet for the other three models, when the ratio of
intra-cluster links and the inter-cluster links reaches certain
quantity, the clustering synchronizability reaches maximal. 相似文献
6.
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
7.
Markus Brede 《Physics letters. A》2008,372(15):2618-2622
In this Letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling network to its synchronizability. These relations were previously only established from a linear stability analysis of the identical oscillator case. We further demonstrate that the heterogeneity in the oscillator population produces heterogeneity in the optimal coupling network as well. Two rules for enhancing the synchronizability of a given network by a suitable placement of oscillators are given: (i) native frequencies of adjacent oscillators must be anti-correlated and (ii) frequency magnitudes should positively correlate with the degree of the node they are placed at. 相似文献
8.
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
9.
Representation of quantum states by statistical ensembles on the quantum phase space in the Hamiltonian form of quantum mechanics is analyzed. Various mathematical properties and some physical interpretations of the equivalence classes of ensembles representing a mixed quantum state in the Hamiltonian formulation are examined. In particular, non-uniqueness of the quantum phase space probability density associated with the quantum mixed state, Liouville dynamics of the probability densities and the possibility to represent the reduced states of bipartite systems by marginal distributions are discussed in detail. These considerations are used to study ensembles of hybrid quantum-classical systems. In particular, nonlinear evolution of a single hybrid system in a pure state and unequal evolutions of initially equivalent ensembles are discussed in the context of coupled hybrid systems. 相似文献
10.
Adaptive dynamical networks via neighborhood information: synchronization and pinning control 总被引:1,自引:0,他引:1
Lu W 《Chaos (Woodbury, N.Y.)》2007,17(2):023122
In this paper, we introduce a model of an adaptive dynamical network by integrating the complex network model and adaptive technique. In this model, the adaptive updating laws for each vertex in the network depend only on the state information of its neighborhood, besides itself and external controllers. This suggests that an adaptive technique be added to a complex network without breaking its intrinsic existing network topology. The core of adaptive dynamical networks is to design suitable adaptive updating laws to attain certain aims. Here, we propose two series of adaptive laws to synchronize and pin a complex network, respectively. Based on the Lyapunov function method, we can prove that under several mild conditions, with the adaptive technique, a connected network topology is sufficient to synchronize or stabilize any chaotic dynamics of the uncoupled system. This implies that these adaptive updating laws actually enhance synchronizability and stabilizability, respectively. We find out that even though these adaptive methods can succeed for all networks with connectivity, the underlying network topology can affect the convergent rate and the terminal average coupling and pinning strength. In addition, this influence can be measured by the smallest nonzero eigenvalue of the corresponding Laplacian. Moreover, we provide a detailed study of the influence of the prior parameters in this adaptive laws and present several numerical examples to verify our theoretical results and further discussion. 相似文献
11.
《Physics letters. A》2014,378(18-19):1239-1248
Synchronization is one of the most important features observed in large-scale complex networks of interacting dynamical systems. As is well known, there is a close relation between the network topology and the network synchronizability. Using the coupled Hindmarsh–Rose neurons with community structure as a model network, in this paper we explore how failures of the nodes due to random errors or intentional attacks affect the synchronizability of community networks. The intentional attacks are realized by removing a fraction of the nodes with high values in some centrality measure such as the centralities of degree, eigenvector, betweenness and closeness. According to the master stability function method, we employ the algebraic connectivity of the considered community network as an indicator to examine the network synchronizability. Numerical evidences show that the node failure strategy based on the betweenness centrality has the most influence on the synchronizability of community networks. With this node failure strategy for a given network with a fixed number of communities, we find that the larger the degree of communities, the worse the network synchronizability; however, for a given network with a fixed degree of communities, we observe that the more the number of communities, the better the network synchronizability. 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.
In this paper networks that optimize a combined measure of local and global synchronizability are evolved. It is shown that
for low coupling improvements in the local synchronizability dominate network evolution. This leads to an expressed grouping
of elements with similar native frequency into cliques, allowing for an early onset of synchronization, but rendering full
synchronization hard to achieve. In contrast, for large coupling the network evolution is governed by improvements towards
full synchronization, preventing any expressed community structure. Such networks exhibit strong coupling between dissimilar
oscillators. Albeit a rapid transition to full synchronization is achieved, the onset of synchronization is delayed in comparison
to the first type of networks. The paper illustrates that an early onset of synchronization (which relates to clustering)
and global synchronization are conflicting demands on network topology. 相似文献
14.
In this paper we propose two methods for altering the synchronizability of scale-free networks: (1) adding edges between the max-degree nodes and min-degree nodes; (2) deleting edges between the max-degree nodes and max-degree nodes. After adding and deleting edges, we find that the former, adding process can weaken synchronizability, while the latter, deleting process can enhance it; the two processes (adding and deleting) can preserve the scale-free structure; the study of the average clustering coefficient indicates that it is not the most closely correlated with the synchronizability among the topological features considered. Our work also suggests that there are some essential relations between the network synchronization and the dynamics of economic systems. They can be used to deal with some problems in the real world, such as relieving the economic crisis. In addition, the adding and deleting processes may have potential applications in modifying network structure, in view of their low cost. 相似文献
15.
There has been mounting evidence that many types of biological or technological networks possess a clustered structure. As many system functions depend on synchronization, it is important to investigate the synchronizability of complex clustered networks. Here we focus on one fundamental question: Under what condition can the network synchronizability be optimized? In particular, since the two basic parameters characterizing a complex clustered network are the probabilities of intercluster and intracluster connections, we investigate, in the corresponding two-dimensional parameter plane, regions where the network can be best synchronized. Our study yields a quite surprising finding: a complex clustered network is most synchronizable when the two probabilities match each other approximately. Mismatch, for instance caused by an overwhelming increase in the number of intracluster links, can counterintuitively suppress or even destroy synchronization, even though such an increase tends to reduce the average network distance. This phenomenon provides possible principles for optimal synchronization on complex clustered networks. We provide extensive numerical evidence and an analytic theory to establish the generality of this phenomenon. 相似文献
16.
Nicolò Musmeci Stefano Battiston Guido Caldarelli Michelangelo Puliga Andrea Gabrielli 《Journal of statistical physics》2013,151(3-4):720-734
In this paper we present a novel method to reconstruct global topological properties of a complex network starting from limited information. We assume to know for all the nodes a non-topological quantity that we interpret as fitness. In contrast, we assume to know the degree, i.e. the number of connections, only for a subset of the nodes in the network. We then use a fitness model, calibrated on the subset of nodes for which degrees are known, in order to generate ensembles of networks. Here, we focus on topological properties that are relevant for processes of contagion and distress propagation in networks, i.e. network density and k-core structure, and we study how well these properties can be estimated as a function of the size of the subset of nodes utilized for the calibration. Finally, we also study how well the resilience to distress propagation in the network can be estimated using our method. We perform a first test on ensembles of synthetic networks generated with the Exponential Random Graph model, which allows to apply common tools from statistical mechanics. We then perform a second test on empirical networks taken from economic and financial contexts. In both cases, we find that a subset as small as 10 % of nodes can be enough to estimate the properties of the network along with its resilience with an error of 5 %. 相似文献
17.
In this paper, we propose a simple weighted network model that generalizes the complex network model evolution with traffic flow previously presented to investigate the relationship between traffic flow and network structure. In the model, the nodes in the network are represented by the traffic flow states, the links in the network are represented by the transform of the traffic flow states, and the traffic flow transported when performing the transform of the traffic flow states is considered as the weight of the link. Several topological features of this generalized weighted model, such as the degree distribution and strength distribution, have been numerically studied. A scaling behavior between the strength and degree s∼klogk is obtained. By introducing some constraints to the generalized weighted model, we study its subnetworks and find that the scaling behavior between the strength and degree is conserved, though the topology properties are quite sensitive to the constraints. 相似文献
18.
Homogeneous entangled networks characterized by small world, large girths, and no community structure have attracted much attention due to some of their favorable performances. However, the optimization algorithm proposed by Donetti et al. is very time-consuming and will lose its efficiency when the size of the target network becomes large. In this paper, an alternative optimization algorithm is provided to get optimal symmetric networks by minimizing the average shortest path length. It is shown that the synchronizability of a symmetric network is enhanced when the average shortest path length of the network is shortened as the optimization proceeds, which suggests that the optimal symmetric networks in terms of minimizing average shortest path length will be very close to those entangled networks. In order to overcome the time-consuming obstacle of the optimization algorithms proposed by us and Donetti et al., a growth model is proposed to get large scale sub-optimal symmetric networks. Numerical simulations show that the symmetric networks derived by our growth model will have small-world property, and besides, these networks will have many other similar favorable performances as entangled networks, e.g., robustness against errors and attacks, very good load balancing ability, and strong synchronizability. 相似文献
19.
Dmytro Kharchenko Vasyl Kharchenko Iryna Lysenko 《Central European Journal of Physics》2011,9(3):698-709
We apply the phase field crystal method for nonequilibrium patterning to stochastic systems with an external source in which
transient dynamics is essential. Considering a prototype model for a one-component periodic system subjected to external influence
kind of irradiation we study properties of pattern selection processes and external noise induced pattern-forming transitions.
These processes are examined by means of the structure function dynamics analysis. Nonequilibrium pattern-forming transitions
are analyzed numerically. 相似文献
20.
In this paper, the relationship between network
synchronizability and the edge-addition of its associated graph is
investigated. First, it is shown that adding one edge to a cycle
definitely decreases the network synchronizability. Then, since
sometimes the synchronizability can be enhanced by changing the
network structure, the question of whether the networks with more
edges are easier to synchronize is addressed. Based on a subgraph
and complementary graph method, it is shown by examples that the
answer is negative even if the network structure is arbitrarily
optimized. This reveals that generally there are redundant edges in
a network, which not only make no contributions to synchronization
but actually may reduce the synchronizability. Moreover, a simple
example shows that the node betweenness centrality is not always a
good indicator for the network synchronizability. Finally, some more
examples are presented to illustrate how the network
synchronizability varies following the addition of edges, where all
the examples show that the network synchronizability globally
increases but locally fluctuates as the number of added edges
increases. 相似文献