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Does the eigenratio λ<sub>2</sub>/λ<sub>N</sub> represent the synchronizability of a complex network? 下载免费PDF全文
In the study of complex networks,it is commonly believed that the eigenratio λ2/λ N of the Laplacian matrix of a network represents the network synchronizability,especially for symmetric networks.This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region.Consequently,a simple answer is presented to the question of when the eigenratio λ2/λ N does represent the network synchronizability. 相似文献
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图论与复杂网络 总被引:1,自引:0,他引:1
近10年来迅猛发展起来的复杂网络理论为研究复杂性与复杂系统科学提供了一个重要支撑点,它高度概括了复杂系统的重要特征,无论是在理论还是在应用方面都具有很强的生命力,而且在各个方面都得到了很大发展.重点讨论图论在复杂网络中的应用,特别是代数图论在复杂网络同步问题中的应用.首先给出一些图的最小非零与最大特征值以及同步能力的估计,并且讨论了子图与图特征向量在同步能力估计中的作用.其次以两个简单图指出同步能力与网络结构参数的关系复杂,并给出补图与加边对同步研究的意义,然后给出图运算在复杂网络同步中的作用.最后从图论与控制理论角度展望了复杂网络领域未来可能的发展方向. 相似文献
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The influence of structural properties of a network on the network synchronizability is studied by introducing a new concept of average range of edges. For both small-world and scale-free networks, the effect of average range on the synchronizability of networks with bounded or unbounded synchronization regions is illustrated through numerical simulations. The relations between average range, range distribution, average distance, and maximum betweenness are also explored, revealing the effects of these factors on the network synchronizability of the small-world and scale-free networks, respectively. 相似文献
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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
5.
The problem of pinning control for the synchronization of complex
dynamical networks is discussed in this paper. A cost function of
the controlled network is defined by the feedback gain and the
coupling strength of the network. An interesting result is that a
lower cost is achieved by using the control scheme of pinning nodes
with smaller degrees. Some strict mathematical analyses are
presented for achieving a lower cost in the synchronization of
different star-shaped networks. Numerical simulations on some
non-regular complex networks generated by the Barabási--Albert
model and various star-shaped networks are performed for
verification and illustration. 相似文献
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In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are
demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can
spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence. 相似文献
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In the study of complex networks, it is commonly believed that the eigenratio λ2/λN of the Laplacian matrix of a network represents the network synchronizability, especially for symmetric networks. This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region. Consequently, a simple answer is presented to the question of when the eigenratio λ2/λN does represent the network synchronizability. 相似文献
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This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances.A dynamical network is said to be robust to disturbance,if the H ∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small.It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H ∞ control problem of a set of independent systems whose dimensions are equal to that of a single node.A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node.To improve this,local feedback injections are applied to a small fraction of the nodes in the network.Some criteria for possible performance improvement are derived in terms of linear matrix inequalities.It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees. 相似文献
10.
In the study of complex networks,it is commonly believed that the eigenratio λ2/λ N of the Laplacian matrix of a network represents the network synchronizability,especially for symmetric networks.This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region.Consequently,a simple answer is presented to the question of when the eigenratio λ2/λ N does represent the network synchronizability. 相似文献
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