Stability and dynamical properties of material flow systems on random networks
Department of Mathematics, King's College London, Strand, London WC2R2, LS, UK
2 School of Physics and Astronomy, The University of Manchester, Manchester M139, PL, UK
Corresponding author: a Kartik.firstname.lastname@example.org
Published online: 25 March 2009
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability.
PACS: 64.60.aq – Networks / 64.60.De – Statistical mechanics of model systems / 89.65.Gh – Economics; econophysics, financial markets, business and management
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009