Analytical solution for a class of network dynamics with mechanical and financial applications
Statistical Mechanics
2014-10-17 v2 Disordered Systems and Neural Networks
Social and Information Networks
Physics and Society
Statistical Finance
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.
Cite
@article{arxiv.1309.4050,
title = {Analytical solution for a class of network dynamics with mechanical and financial applications},
author = {Pavel Krejčí and Harbir Lamba and Sergey Melnik and Dmitrii Rachinskii},
journal= {arXiv preprint arXiv:1309.4050},
year = {2014}
}
Comments
12 pages, 9 figures, 1 table