Topologically controlled emergent dynamics in flow networks

TL;DR

This paper introduces a model for flow networks with nonlinear conductance that exhibit self-sustained wave dynamics driven purely by network topology, without inherent oscillatory node behavior.

Contribution

It demonstrates how complex emergent wave dynamics can arise from topology in flow networks with nonlinear conductance, independent of node oscillations.

Findings

Emergent self-sustained waves depend on network architecture.

Wave frequency correlates with a topological metric.

Dynamics occur without inherent node oscillations or excitability.

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.