Analytical Solution for a Class of Network Dynamics with Mechanical and Financial Applications




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Published By The American Physical Society Through The American Institute Of Physics


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.



Network analysis (Planning)--Mathematical models, Prandtl-Ishlinskii model, Precision-recall curves, Prices

GAČR (Grant No. P201/10/2315 and RVO 67985840); Science Foundation Ireland (Grant No. 11/PI/1026); US National Science Foundation (Grant No. DMS-1413223).


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