  Network theory is rapidly changing our understanding of complex systems, but
the relevance of topological features for the dynamic behavior of metabolic
networks, food webs, production systems, information networks, or cascade
failures of power grids remains to be explored. Based on a simple model of
supply networks, we offer an interpretation of instabilities and oscillations
observed in biological, ecological, economic, and engineering systems.
  We find that most supply networks display damped oscillations, even when
their units - and linear chains of these units - behave in a non-oscillatory
way. Moreover, networks of damped oscillators tend to produce growing
oscillations. This surprising behavior offers, for example, a new
interpretation of business cycles and of oscillating or pulsating processes.
The network structure of material flows itself turns out to be a source of
instability, and cyclical variations are an inherent feature of decentralized
adjustments. In particular, we show how to treat production and supply networks
as transport problems governed by balance equations and equations for the
adaptation of production speeds.
  The stability and dynamic behavior of supply networks is investigated for
different topologies, including sequential supply chains, "supply circles",
"supply ladders", and "supply hierarchies". Moreover, analytical conditions for
absolute and convective instabilities are derived. The empirically observed
bullwhip effect in supply chains is explained as a form of convective
instability based on resonance effects. An application of this theory to the
optimization of production networks has large optimization potentials.
