0433123 - MÚ 2015 RIV US eng J - Journal Article
Krejčí, Pavel - Lamba, H. - Melnik, S. - Rachinskii, D.
Analytical solution for a class of network dynamics with mechanical and financial applications.
Physical Review E. Roč. 90, č. 3 (2014), 032822. ISSN 1539-3755. E-ISSN 2470-0053
R&D Projects: GA ČR GAP201/10/2315
Institutional support: RVO:67985840
Keywords : network dynamics * hysteresis * discontinuous Prandtl-Ishlinskii model
Subject RIV: BA - General Mathematics
Impact factor: 2.288, year: 2014
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.032822

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.
Permanent Link: http://hdl.handle.net/11104/0237392