Abstract
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 networks, we offer an interpretation of instabilities and oscillations observed in biological, ecological, economic, and engineering systems. We find that most 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 networks as transport problems governed by balance equations and equations for the adaptation of production speeds. The stability and dynamic behavior of networks is investigated for different topologies, including sequential chains, supply circles, supply ladders, and supply hierarchies. Moreover, analytical conditions for absolute and convective instabilities are derived. The empirically observed bullwhip effect in 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.
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