Analytical solution for a class of network dynamics with mechanical and financial applications
arXiv:1309.4050 · doi:10.1103/PhysRevE.90.032822
Abstract
We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces, and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.
arXiv comment12 pages, 9 figures, 1 table
References in corpus (12)
- Power-law distributions in empirical data
- Epidemic spreading in scale-free networks
- Statistical physics of social dynamics
- Crackling Noise
- Scaling of the distribution of fluctuations of financial market indices
- Thresholds for epidemic spreading in networks
- Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
- Ising Model on Networks with an Arbitrary Distribution of Connections
- High-accuracy approximation of binary-state dynamics on networks
- Epidemic threshold for the SIS model on networks
- Crackling Noise in Fractional Percolation -- Randomly distributed discontinuous jumps in explosive percolation
- A queueing theory description of fat-tailed price returns in imperfect financial markets