2004/05/11 by Dirk Helbing, Stefan Lammer, Stefan Lämmer +6
Computer Science · Environmental Science · Physics and Astronomy · #Ecosystem dynamics and resilience #Nonlinear Dynamics and Pattern Formation #Sustainability and Ecological Systems Analysis #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.70.066116
published as Physical Review E 70, 066116 (2004) · For related work see http://www.helbing.org
arxiv created 2004/05/11 · openalex publication_date 2004/12/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bullwhip 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 damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.