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Topologically controlled emergent dynamics in flow networks

We present a model for flow networks with non-linear conductance that allows for internal accumulation/depletion of volume. 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. These spontaneously emerging fluctuations persist for a broad range of network topologies and system parameters. The frequency of the self-sustained waves depends strongly on the network architecture and it can be explained with a topological metric.