Organization of excitable dynamics in hierarchical networks - Theoretical analysis, numerical simulation and application to neuroscience

层次结构是生物网络，特别是神经网络的一个明显特征，但人们对它的了解却很少。我们将描述不同类型的层次网络，并确定最强烈地塑造其功能动力学的拓扑参数。此外，我们将确定哪些参数是不变的粗粒度和细粒度的网络，由于其层次结构，并研究如何在节点级别的不同的可激发机制影响全球网络动态。对于一个大的和生物学上重要的一类可兴奋网络，因此，我们希望获得一个深刻的理论理解网络拓扑结构和动力学过程如何相互作用。

Hierarchy is an obvious, but only minimally understood feature of biological, and particularly neural, networks. We will characterize different types of hierarchical networks and identify the topological parameters that most strongly shape their functional dynamics. Moreover, we will determine which of the parameters are invariant to coarse- and fine-graining of the networks due to their hierarchical structure, and investigate how different excitable mechanisms at the node level affect the global network dynamics. For a large and biologically important class of excitable networks, we thus want to obtain a deep theoretical understanding of how network topology and dynamical processes interact.