title: Analytical solution for a class of network dynamics with mechanical and financial applications.
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.
authors.affiliation: Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague, Czech Republic.
authors.forename: P
authors.initials: P
authors.lastname: Krejčí
authors.affiliation: Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA.
authors.forename: H
authors.initials: H
authors.lastname: Lamba
authors.affiliation: MACSI, Department of Mathematics & Statistics, University of Limerick, Limerick, Ireland.
authors.forename: S
authors.initials: S
authors.lastname: Melnik
authors.affiliation: Department of Applied Mathematics, University College Cork, Western Road, Cork, Ireland and Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75080, USA.
authors.forename: D
authors.initials: D
authors.lastname: Rachinskii
mesh_terms: D003198:Computer Simulation; D004548:Elasticity; D005376:Financial Management; D017276:Friction; D008962:Models, Theoretical; D010969:Plastics
chemical_list: D010969:Plastics