  We show how to treat supply networks as physical transport problems governed
by balance equations and equations for the adaptation of production speeds.
Although the non-linear behaviour is different, the linearized set of coupled
differential equations is formally related to those of mechanical or electrical
oscillator networks. Supply networks possess interesting new features due to
their complex topology and directed links. We derive analytical conditions for
absolute and convective instabilities. The empirically observed "bull-whip
effect" in supply chains is explained as a form of convective instability based
on resonance effects. Moreover, it is generalized to arbitrary supply networks.
Their related eigenvalues are usually complex, depending on the network
structure (even without loops). Therefore, their generic behavior is
characterized by oscillations. We also show that regular distribution networks
possess two negative eigenvalues only, but perturbations generate a spectrum of
complex eigenvalues.

Statistical Mechanics;Disordered Systems and Neural Networks