Robust dynamical effects in traffic and chaotic maps on trees

Abstract

In the dynamic processes on networks collective effects emerge due to the couplings between nodes, where the network structure may play an important role. Interaction along many network links in the nonlinear dynamics may lead to a kind of chaotic collective behavior. Here we study two types of well-defined diffusive dynamics on scale-free trees: traffic of packets as navigated random walks, and chaotic standard maps coupled along the network links. We show that in both cases robust collective dynamic effects appear, which can be measured statistically and related to non-ergodicity of the dynamics on the network. Specifically, we find universal features in the fluctuations of time series and appropriately defined return-time statistics.

When Does a Child 'Participate Actively in Hostilities' under the Rome Statute? Protecting Children from Use in Hostilities after Lubanga

“…or, in the case of internal armed conflicts, a peaceful settlement is achieved. 186 The violence of any armed conflict must be more than sporadic in the case of a non-international armed conflict. 187 The Lubanga Trial Chamber endorsed the ICTY's approach to determining whether a conflict was an armed conflict or not: 188 the intensity of the conflict should be used 'solely as a way to distinguish an armed conflict from banditry, unorganised and short-lived insurrections, or terrorist activities, which are not subject to international humanitarian law.'…”