复杂网络上接触过程的慢动力学
Slow dynamics of the contact process on complex networks
摘要：
本文研究了具有不同淬火无序的复杂网络的接触过程。数值证据发现格里菲斯阶段和其他罕见的区域效应，在Erd \H OS雷尼网络，而导致一般的缓慢（代数，对数，.）放松.更令人惊讶的是，格里菲斯相也可以在没有淬火无序的情况下出现，这是有限拓扑维数网络中唯一拓扑异质性的结果。在无标度网络的情况下，表现出无限的拓扑维数，可以观察到缓慢的动态树状结构和叠加的重量模式。在无限大的极限下，顶点的关联子空间似乎会引起模糊的相变。这些结果对网络中的传播现象和其他动力学过程具有广泛的意义，并且对于模型和经验数据的分析都是相关的。
英文摘要：
The Contact Process has been studied on complex networks exhibiting different kinds of quenched disorder. Numerical evidence is found for Griffiths phases and other rare region effects, in Erd\H os Rényi networks, leading rather generically to anomalously slow (algebraic, logarithmic,...) relaxation. More surprisingly, it turns out that Griffiths phases can also emerge in the absence of quenched disorder, as a consequence of sole topological heterogeneity in networks with finite topological dimension. In case of scale-free networks, exhibiting infinite topological dimension, slow dynamics can be observed on tree-like structures and a superimposed weight pattern. In the infinite size limit the correlated subspaces of vertices seem to cause a smeared phase transition. These results have a broad spectrum of implications for propagation phenomena and other dynamical process on networks and are relevant for the analysis of both models and empirical data.
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