Generic phase transitions and profit singularities in Arnol'd's model

Davydov, A.A. & Mena-Matos, H. (2007). Generic phase transitions and profit singularities in Arnol'd's model. Sbornik: Mathematics 198 (1) 21-42. 10.1070/SM2007v198n01ABEH003827.

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Abstract

For a smooth one-parameter family of pairs of control systems and profit densities on a circle, the generic transitions between optimal rotations and stationary strategies are studied in the problem of maximization of the time-averaged profit on the infinite horizon. It is shown that there are only two types of such transitions, the corresponding singularities of the average profit as a function of the family parameter are found, and it is proved that these singularities are stable under small perturbations of a generic family. The classification of singularities of the maximum average profit is completed for generic families.

Item Type:	Article
Research Programs:	Dynamic Systems (DYN)
Bibliographic Reference:	Sbornik: Mathematics; 198(1):21-42 [2007]
Depositing User:	IIASA Import
Date Deposited:	15 Jan 2016 08:39
Last Modified:	27 Aug 2021 17:38
URI:	https://pure.iiasa.ac.at/8109

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