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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
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A Chaotic Communication Scheme Based on Generalized Synchronization and Hash Functions 总被引:6,自引:0,他引:6 下载免费PDF全文
A new chaotic communication scheme based on generalized chaotic synchronization (GCS) and hash function transpositions is presented. The communication scheme has nonsymmetric secrete keys and its ability is similar to traditional digital signatures, i.e. a receiver can convince himself whether or not the sender‘s message contents have been modified. As a direct application of the scheme, a GCS system is designed by using Chen‘s chaotic circuit and is studied in some detail. The numerical simulation shows that this Chen GCS system has high security and is fast and reliable for secure lnternet communications. 相似文献
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研究Banach 空间上连续 Frechét可微映射导出 的离散动力系统之混沌. 建立一个由正则非退化同宿轨道产生混沌的判定定理, 并对n维实空间上的离散动力系统的混沌进行了讨论, 建立了两个由非退化返回扩张不动点产生混沌的判定定理, 其中一个为Marotto 定理的修正定理. 特别地, 分别给出了一般 Banach 空间及n维实空间上的连续可微映射不动点为扩张的充分必要条件, 彻底解决了多年以来人们对n上连续可微映射不动点的扩张性与其 Jacobi矩阵特征值之间关系的困惑. 相似文献
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该文基于马氏链的概念和技巧, 给出了BA无标度网络模型稳态度分布存在性的严格证明, 并且从数学上重新推导了度分布的精确解析表达式. 此处所用的方法具有一定的普适性, 适用于更一般的无标度型复杂网络模型. 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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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