复杂网络上的突发性与分数扩散
Burstiness and fractional diffusion on complex networks
摘要：
现实世界网络中的许多动态过程显示出复杂的时间模式，例如，事件间时间的厚尾分布，导致事件之间的异质等待时间。在这项工作中，我们专注于平均事件间时间发散的分布，并研究其对网络上随机游走者动力学的影响。在长时间限制下，这个过程自然可以用黎曼-刘维尔分数阶导数来描述。我们发现，所有的动力学模式具有，在渐近制度，相同的幂律松弛，这意味着动态不表现出模式之间的时间尺度分离，并且没有模式可以忽略与另一个，即使很长一段时间。我们的结果，然后通过数值模拟证实。
英文摘要：
Many dynamical processes on real world networks display complex temporal patterns as, for instance, a fat-tailed distribution of inter-events times, leading to heterogeneous waiting times between events. In this work, we focus on distributions whose average inter-event time diverges, and study its impact on the dynamics of random walkers on networks. The process can naturally be described, in the long time limit, in terms of Riemann-Liouville fractional derivatives. We show that all the dynamical modes possess, in the asymptotic regime, the same power law relaxation, which implies that the dynamics does not exhibit time-scale separation between modes, and that no mode can be neglected versus another one, even for long times. Our results are then confirmed by numerical simulations.
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