Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a nonlinear relation between current and pressure difference, and can be applied to networks of arbitrary topology. The model displays complex dynamics, including self-sustained oscillations in the absence of any dynamics in the inputs and outputs. In this work we analytically show the origin of self-sustained oscillations for the one-dimensional case. We numerically study the behavior of systems of arbitrary topology under different conditions: we discuss their excitability, the effect of different boundary conditions, and wave propagation when the network has regions of conduits with linear conductance.