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Tr. Mat. Inst. Steklova, 2005, Volume 250, Pages 79–94 (Mi tm32)  

This article is cited in 11 scientific papers (total in 11 papers)

Generic Profit Singularities in Arnold's Model of Cyclic Processes

A. A. Davydovab

a Vladimir State University
b International Institute for Applied Systems Analysis

Abstract: Generic singularities of the maximum time-averaged profit are classified for a one-parameter smooth pair of families of profit densities and control systems with positive velocities on the circle. For example, a typical passage of this profit through a local nondegenerate extremum of the profit density under the change of the parameter yields the singularity $(|p|^{3/2}\pm \nobreak p^2)(1+\mathop {\mathrm {sgn}} p)$ of the profit up to a diffeomorphism of its graph space fibered over the parameter.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 250, 70–84

Bibliographic databases:

UDC: 517.977.1
Received in January 2005

Citation: A. A. Davydov, “Generic Profit Singularities in Arnold's Model of Cyclic Processes”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 250, Nauka, MAIK Nauka/Inteperiodika, M., 2005, 79–94; Proc. Steklov Inst. Math., 250 (2005), 70–84

Citation in format AMSBIB
\by A.~A.~Davydov
\paper Generic Profit Singularities in Arnold's Model of Cyclic Processes
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2005
\vol 250
\pages 79--94
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 250
\pages 70--84

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    This publication is cited in the following articles:
    1. Davydov A.A., Mena Matos E., “Optimal strategies and transitions between them in Arnold's model”, Dokl. Math., 74:1 (2006), 566–568  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. A. A. Davydov, H. Mena Matos, “Generic phase transitions and profit singularities in Arnol'd's model”, Sb. Math., 198:1 (2007), 17–37  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Mena-Matos H., Moreira C., “Generic singularities of the optimal averaged profit among stationary strategies”, J. Dyn. Control Syst., 13:4 (2007), 541–562  crossref  mathscinet  zmath  isi  elib  scopus
    4. Davydov A., Mena-Matos H., “Singularity theory approach to time averaged optimization”, Singularities in Geometry and Topology, 2005, 2007, 598–628  crossref  mathscinet  zmath  isi
    5. A. A. Davydov, T. S. Shutkina, “Optimizing a cyclic process with discount with respect to its time average profit”, Russian Math. Surveys, 64:1 (2009), 136–138  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Mena-Matos H., “Generic profit singularities in time averaged optimization. The case of a control space with a regular boundary”, J. Dyn. Control Syst., 16:1 (2010), 101–120  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. A. Davydov, T. S. Shutkina, “Optimizatsiya tsiklicheskikh protsessov s diskontirovaniem po usiliyu i vygode”, Nelineinaya dinam., 6:1 (2010), 151–158  mathnet  elib
    8. A. A. Davydov, T. S. Shutkina, “Uniqueness of a cycle with discounting that is optimal with respect to the average time profit”, Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S80–S87  mathnet  crossref  isi  elib
    9. A. A. Davydov, H. Mena-Matos, C. S. Moreira, “Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems”, Journal of Mathematical Sciences, 199:5 (2014), 510–534  mathnet  crossref  mathscinet
    10. Davydov A.A., Mena-Matos H., Moreira C.S., “Generic Profit Singularities in Time Averaged Optimization For Phase Transitions in Polydynamical Systems”, J. Math. Anal. Appl., 424:1 (2015), 704–726  crossref  mathscinet  zmath  isi  elib  scopus
    11. A. Belyakov, A. A. Davydov, “Efficiency optimization for the cyclic use of a renewable resource”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 14–21  mathnet  crossref  crossref  mathscinet  isi  elib
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