Stability and dynamical properties of material flow systems on random networks

Abstract

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.

15 pages, 13 figures

References in corpus (20)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Scaling and percolation in the small-world network model
• Spectra of complex networks
• Sparse random matrices: the eigenvalue spectrum revisited
• Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
• Spectra of Sparse Random Matrices
• A single defect approximation for localized states on random lattices
• Physics, Stability and Dynamics of Supply Networks
• Network-Induced Oscillatory Behavior in Material Flow Networks
• Lifshitz tails for spectra of Erdős--Rényi random graphs
• Spectral Density of Sparse Sample Covariance Matrices
• Phase Transitions in Operational Risk
• Effects of Economic Interactions on Credit Risk
• Typical properties of optimal growth in the Von Neumann expanding model for large random economies
• Slowly evolving geometry in recurrent neural networks I: extreme dilution regime
• Evolving eco-system: a network of networks
• Stability and dynamical properties of material flow systems on random networks
• Spectral properties of complex networks
• Modeling Evolving Innovation Networks

Cited by in corpus (4)

• Eigenvalues of random matrices with generalised correlations: a path integral approach
• Exact solution of Dynamical Mean-Field Theory for a linear system with annealed disorder
• A maximum entropy network reconstruction of macroeconomic models
• Stability and dynamical properties of material flow systems on random networks