Topologically controlled emergent dynamics in flow networks

Abstract: Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks interconnecting explicitly oscillatory or excitable elements can display rich emerging dynamics. Here we present a model for complex flow networks with non-linear conductance that allows for internal accumulation/depletion of volume, without any inherent oscillatory or excitable behavior at the nodes. In the absence of any time dependence in the pressure input and output we observe emerging dynamics in the form of self-sustained waves, which travel through the system. The frequency of these waves depends strongly on the network architecture and it can be explained with a topological metric.