  Coherent, large scale dynamics in many nonequilibrium physical, biological,
or information transport networks are driven by small-scale local energy input.
Here, we introduce and explore an analytically tractable nonlinear model for
compressible active flow networks. In contrast to thermally-driven systems, we
find that active friction selects discrete states with a limited number of
oscillation modes activated at distinct fixed amplitudes. Using perturbation
theory, we systematically predict the stationary states of noisy networks and
find good agreement with a Bayesian state estimation based on a hidden Markov
model applied to simulated time series data. Our results suggest that the
macroscopic response of active network structures, from actomyosin force
networks to cytoplasmic flows, can be dominated by a significantly reduced
number of modes, in contrast to energy equipartition in thermal equilibrium.
The model is also well-suited to study topological sound modes and spectral
band gaps in active matter.
