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Davydov Alexey Alexandrovich

Statistics Math-Net.Ru
Total publications: 37
Scientific articles: 31
Presentations: 12

Number of views:
This page:6220
Abstract pages:14278
Full texts:3039
References:1242
Professor
Doctor of physico-mathematical sciences (1993)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 20.09.1956
Phone: +7 (4922) 479726
Fax: +7 (4922) 233342
E-mail: ,
Keywords: singularity, normal form, structural stability, parametric optimization.
UDC: 512.737, 517.9, 517.91, 517.977.1, 515.1, 517.958, 517.977, 519.63, 517.938
MSC: 49J15, 49J45, 49N20, 49N60, 58K25, 58K40, 90C31

Subject:

Singularity theory, differential equation, mathematical control theory.

Biography

Alexey Davydov joined IIASA in January 2005 as Principal Investigator within the Dynamic Systems Program.
Prof. Davydov received his master's degree in mathematics in 1979, his candidate degree (Ph.D.) in physics and mathematics in 1983, both from Moscow State University, and his doctorate in physics and mathematics from the Steklov Institute of Mathematics in 1993 with his dissertation on implicit differential equations and qualitative theory of control systems. His scientific interests include ordinary differential equations, dynamic systems with control, singularity theory, and parametric optimization. He has authored more than forty scientific papers and the monograph "Qualitative Theory of Control Systems," MIR - AMS, 1994. Since 1982 he has worked at the Vladimir State University as an Assistant Professor (1982–1984), Associate Professor (1984–1990), and Full Professor (1993–present). From 1990 to 1993 he occupied a research position at the Steklov Institute of Mathematics.
Prof. Davydov received the Moscow Mathematical Society Award (1986) and the International Academic Publishing Company Prize (2002). He was visiting professor and research fellow at the Universidad Nacional Autonoma de Mexico, RTWH-Aachen, Universidade do Porto, Paris VII, and Hokkaido University, and has participated in several international scientific projects.

   
Main publications:
  1. Davydov A.A., “Normalnaya forma differentsialnogo uravneniya uravneniya, ne razreshennogo otnositelno proizvodnoi v okrestnosti ego osoboi tochki”, Funkts. analiz i ego prilozheniya, 19:2 (1985), 1–10  mathnet  mathscinet  zmath
  2. Davydov A.A., “Osobennosti polei predelnykh napravlenii dvumernykh upravlyaemykh sistem”, Matem. sb., 136(178):4 (1988), 478–499  mathnet  mathscinet  zmath
  3. Davydov A.A., “Strukturnaya ustoichivost upravlyaemykh sistem na orientiruemykh poverkhnostyakh”, Matem. sb., 182:1 (1991), 3–35  mathnet  mathscinet  zmath
  4. Davydov A.A., Rosales-Gonsales E., “Polnaya klassifikatsiya tipichnykh lineinykh differentsialnykh uravnenii vtorogo poryadka s chastnymi proizvodnymi na ploskosti”, Dokl. RAN, 350:2 (1996), 151–154  mathscinet  zmath
  5. Davydov A.A., Mena-Matosh E., “Tipichnye fazovye perekhody i osobennosti vygody v modeli Arnolda”, Matem. sb., 198:1 (2007), 21–42  mathnet  mathscinet  zmath

http://www.mathnet.ru/eng/person8532
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/601545
https://www.researchgate.net/profile/A_Davydov2

Publications in Math-Net.Ru
1. Efficiency optimization for the cyclic use of a renewable resource
A. Belyakov, A. A. Davydov
Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  38–46
2. On the uniqueness of a positive stationary state in the dynamics of a population with asymmetric competition
A. A. Davydov, A. F. Nassar
Tr. Mat. Inst. Steklova, 291 (2015),  86–94
3. On a stationary state in the dynamics of a population with hierarchical competition
A. A. Davydov, A. F. Nassar
Uspekhi Mat. Nauk, 69:6(420) (2014),  179–180
4. Optimal exploitation of two competing size-structured populations
A. A. Davydov, A. S. Platov
Trudy Inst. Mat. i Mekh. UrO RAN, 19:4 (2013),  89–94
5. Optimal stationary solution for a model of exploitation of a population under intraspecific competition
A. A. Davydov, A. S. Platov
CMFD, 46 (2012),  44–48
6. Optimal stationary solution in forest management model by accounting intra-species competition
A. A. Davydov, A. S. Platov
Mosc. Math. J., 12:2 (2012),  269–273
7. Controllability of non-linear systems: generic singularities and their stability
A. A. Davydov, V. M. Zakalyukin
Uspekhi Mat. Nauk, 67:2(404) (2012),  65–92
8. Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems
A. A. Davydov, H. Mena-Matos, C. S. Moreira
CMFD, 42 (2011),  95–117
9. Uniqueness of a cycle with discounting that is optimal with respect to the average time profit
A. A. Davydov, T. S. Shutkina
Trudy Inst. Mat. i Mekh. UrO RAN, 17:2 (2011),  80–87
10. Time average optimization of cycle process with profit and effort discounts
A. A. Davydov, T. S. Shutkina
Nelin. Dinam., 6:1 (2010),  151–158
11. Normal forms for families of linear equations of mixed type near non-resonant folded singular points
A. A. Davydov, L. Trinh Thi Diep
Uspekhi Mat. Nauk, 65:5(395) (2010),  189–190
12. Optimization of the spatial distribution of pollution emission in 1D flow
A. Davydov, R. Pastres, I. Petrenko
Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010),  30–35
13. Optimizing a cyclic process with discount with respect to its time average profit
A. A. Davydov, T. S. Shutkina
Uspekhi Mat. Nauk, 64:1(385) (2009),  143–144
14. Existence and Uniqueness of a Stationary Distribution of a Biological Community
A. A. Davydov, V. I. Danchenko, M. Yu. Zvyagin
Tr. Mat. Inst. Steklova, 267 (2009),  46–55
15. Local Controllability Bifurcations in Families of Bidynamical Systems on the Plane
A. A. Davydov, M. A. Komarov
Tr. Mat. Inst. Steklova, 261 (2008),  87–96
16. Andronov–Hopf bifurcation in simple double diffusion models
A. A. Davydov, N. B. Melnikov
Uspekhi Mat. Nauk, 62:2(374) (2007),  175–176
17. Generic phase transitions and profit singularities in Arnol'd's model
A. A. Davydov, H. Mena Matos
Mat. Sb., 198:1 (2007),  21–42
18. Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes
A. A. Davydov, N. B. Melnikov
Tr. Mat. Inst. Steklova, 259 (2007),  10–19
19. Structural Stability of Simplest Dynamical Inequalities
Yu. A. Grishina, A. A. Davydov
Tr. Mat. Inst. Steklova, 256 (2007),  89–101
20. Generic Profit Singularities in Arnold's Model of Cyclic Processes
A. A. Davydov
Tr. Mat. Inst. Steklova, 250 (2005),  79–94
21. Singularities of Limiting Directions of Generic Higher Order Implicit ODEs
A. A. Davydov
Tr. Mat. Inst. Steklova, 236 (2002),  134–141
22. Controllability of inequalities at 2-singular points
A. A. Davydov, J. Basto-Goncalves
Uspekhi Mat. Nauk, 55:6(336) (2000),  121–122
23. The coincidence of generic singularities of solutions of extremal problems with constraints
A. A. Davydov, V. M. Zakalyukin
Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 64 (1999),  118–143
24. Point singularities of a conditional minimum on a three-dimensional manifold
A. A. Davydov, V. M. Zakalyukin
Tr. Mat. Inst. Steklova, 220 (1998),  113–129
25. Normal forms of folded elementary singular points
A. A. Davydov, L. Ortiz-Bobadil'ya
Uspekhi Mat. Nauk, 50:6(306) (1995),  175–176
26. Local controllability of typical dynamical inequalities on surfaces
A. A. Davydov
Trudy Mat. Inst. Steklov., 209 (1995),  84–123
27. Structural stability of control systems on orientable surfaces
A. A. Davydov
Mat. Sb., 182:1 (1991),  3–35
28. Singularities of fields of limiting directios of two-dimensional control systems
A. A. Davydov
Mat. Sb. (N.S.), 136(178):4(8) (1988),  478–499
29. The normal form of slow motions of an equation of relaxation type and fibrations of binomial surfaces
A. A. Davydov
Mat. Sb. (N.S.), 132(174):1 (1987),  131–139
30. Normal form of a differential equation, not solvable for the derivative, in a neighborhood of a singular point
A. A. Davydov
Funktsional. Anal. i Prilozhen., 19:2 (1985),  1–10
31. Singularities of the admissibility boundary in two-dimensional control systems
A. A. Davydov
Uspekhi Mat. Nauk, 37:3(225) (1982),  183–184

32. Dmitrii Viktorovich Anosov (obituary)
S. M. Aseev, V. M. Buchstaber, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, A. A. Davydov, A. Yu. Zhirov, E. V. Zhuzhoma, M. I. Zelikin, A. B. Katok, A. V. Klimenko, V. V. Kozlov, V. P. Leksin, M. I. Monastyrskii, A. I. Neishtadt, S. P. Novikov, E. A. Sataev, Ya. G. Sinai, A. M. Stepin
Uspekhi Mat. Nauk, 70:2(422) (2015),  181–191
33. International mathematical conferences and schools for young researchers in Suzdal'
A. A. Davydov, V. V. Kozlov, F. L. Chernous'ko
Uspekhi Mat. Nauk, 69:1(415) (2014),  189–191
34. Vladimir Mikhailovich Zakalyukin (obituary)
A. A. Agrachev, D. V. Anosov, I. A. Bogaevskii, A. S. Bortakovskii, A. B. Budak, V. A. Vassiliev, V. V. Goryunov, S. M. Gusein-Zade, A. A. Davydov, V. R. Zarodov, V. D. Sedykh, D. V. Treshchev, V. N. Chubarikov
Uspekhi Mat. Nauk, 67:2(404) (2012),  187–190
35. In memory of Evgenii Frolovich Mishchenko
Yu. S. Osipov, V. V. Kozlov, L. D. Faddeev, D. V. Anosov, V. S. Vladimirov, R. V. Gamkrelidze, A. A. Gonchar, N. N. Krasovskii, A. V. Kryazhimskii, A. B. Kurzhanskii, S. P. Novikov, S. M. Aseev, A. B. Zhizhchenko, D. V. Treschev, A. A. Agrachev, E. A. Volkov, N. L. Grigorenko, A. A. Davydov, M. I. Zelikin, A. Yu. Kolesov, A. A. Mal'tsev, M. S. Nikol'skii, N. Kh. Rozov, A. G. Sergeev, K. O. Besov, S. P. Konovalov
Tr. Mat. Inst. Steklova, 271 (2010),  7–8
36. Vladimir Igorevich Arnold in the Eyes of His Students: On the occasion of his 70th birthday
A. N. Varchenko, V. A. Vassiliev, S. M. Gusein-Zade, A. A. Davydov, V. M. Zakalyukin, Yu. S. Ilyashenko, M. E. Kazarian, A. G. Kushnirenko, S. K. Lando, A. G. Khovanskii
Tr. Mat. Inst. Steklova, 259 (2007),  5–9
37. Sessions of the Petrovskii seminar on differential equations and mathemathical problems of physics
V. Ya. Rivkind, S. P. Novikov, V. M. Petkov, V. P. Myasnikov, M. V. Fedoryuk, V. V. Kucherenko, A. A. Davydov, A. I. Neishtadt, S. N. Kruzhkov, S. A. Molchanov, A. A. Ruzmaikin, D. D. Sokolov, Yu. M. Sukhov, A. G. Shukhov, B. R. Vainberg, V. I. Bakhtin, A. G. Vainshtein, B. Z. Shapiro, V. A. Kondrat'ev, O. A. Oleinik, M. I. Vishik, S. B. Kuksin, A. G. Korolev, Yu. S. Ilyashenko
Uspekhi Mat. Nauk, 40:5(245) (1985),  295–307

Presentations in Math-Net.Ru
1. Особенности параметрической оптимизации, их устойчивость и приложения
A. A. Davydov
International conference "Systems Analysis: Modeling and Control" in memory of Academician A. V. Kryazhimskiy
May 31, 2018 14:30   
2. Opening of the Conference
N. L. Grigorenko, E. I. Moiseev, A. D. Gvishiani, E. A. Rovenskaya, S. M. Aseev, A. M. Tarasyev, A. A. Davydov, V. I. Maksimov, A. G. Chentsov
International conference "Systems Analysis: Modeling and Control" in memory of Academician A. V. Kryazhimskiy
May 31, 2018 09:30   
3. Mathematical Foundation of Age- and Size-structured Modelling and Control
A. A. Davydov
Age-structured modeling and management of biological and economic resources. Moscow Winter Academy MWA2018
February 6, 2018 09:30   
4. Optimization of stationary solutions in population dynamics
A. A. Davydov
International Conference "Mathematical Theory of Optimal Control" dedicated to the 90th birthday of Academician R. V. Gamkrelidze
June 2, 2017 15:00   
5. К теории нормальных форм уравнений смешанного типа на плоскости
A. A. Davydov
Dynamical systems and differential equations
May 22, 2017 18:30
6. The average time optimization and cyclicity
A. A. Davydov
International conference "Dynamical Systems: Inverse Problems, Stability and Control Processes" dedicated to the 80th birthday of Yu. S. Osipov
September 22, 2016 13:20   
7. Theory of normal forms of linear second order mixed type PDEs on the plane
A. A. Davydov
The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics
May 11, 2016 13:00   
8. Особенности оптимизации циклических процессов
A. A. Davydov
Steklov Mathematical Institute Seminar
February 18, 2016 16:00   
9. Singularities of parametric optimization and optimal control of cyclic processes
A. A. Davydov
International Conference on Mathematical Control Theory and Mechanics
July 5, 2015 12:10
10. Optimal stationary modes of cyclic utilization of renewable resources
A. A. Davydov
The International Conference "Geometric Control Theory and Analysis on Metric Structures"
August 7, 2014 17:00
11. Structural stability of control systems
A. A. Davydov
Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin
September 25, 2013 11:10   
12. Reduction theorem and normal forms of linear second order PDE in the plane
A. A. Davydov
International conference "Analysis and Singularities" dedicated to the 75th anniversary of Vladimir Igorevich Arnold
December 21, 2012 15:40   

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