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:
Davydov A.A., “Normalnaya forma differentsialnogo uravneniya, ne razreshennogo otnositelno proizvodnoi v okrestnosti ego osoboi tochki”, Funkts. analiz i ego prilozheniya, 19:2 (1985), 1–10
Alexey Davydov, Alexander Plakhov, “Dynamics of a Pendulum in a Rarefied Flow”, Regul. Chaotic Dyn., 29:1 (2024), 134–142;
2.
A. A. Davydov, A. S. Platov, D. V. Tunitsky, “Existence of an optimal stationary solution in the KPP model under nonlocal competition”, Trudy Inst. Mat. i Mekh. UrO RAN, 30, no. 3, 2024, 113–121
2023
3.
A. A. Davydov, S. O. Zosimov, “Typical Occurrence of Self-oscillations in an Ocean Circulation Box Model with Turbulent Fluxes”, Proc. Steklov Inst. Math., 321 (2023), 107–116
4.
E. V. Vinnikov, A. A. Davydov, D. V. Tunitsky, “Existence of maximum of time averaged harvesting in the KPP-model on sphere with permanent and impulse collection”, Dokl. Math., 108:3 (2023), 472–476
5.
A. A. Davydov, Kh. A. Khachatryan, “Stationary states in population dynamics with migration and distributed offspring”, CMFD, 69, no. 4, PFUR, M., 2023, 578–587
2022
6.
Davydov, A., Vinnikov, E., “Optimal Cyclic Dynamic of Distributed Population Under Permanent and Impulse Harvesting”, Dynamic Control and Optimization. DCO 2021., Springer Proceedings in Mathematics & Statistics, Springer Proceedings in Mathematics & Statistics, 407, eds. Tchemisova, T.V., Torres, D.F.M., Plakhov, A.Y., Springer, 2022, 90-101
A. A. Davydov, D. A. Melnik, “Optimal states of distributed exploited populations with periodic impulse selection”, Proc. Steklov Inst. Math. (Suppl.), 315, suppl. 1 (2021), S81–S88
8.
A. O. Belyakov, A. A. Davydov, “Optimal Cyclic Harvesting of a Distributed Renewable Resource with Diffusion”, Proc. Steklov Inst. Math., 315 (2021), 56–64
9.
Alexey Davydov, “Optimal steady state of distributed population in periodic environment”, AIP Conference Proceedings, 2333:1, 120007 (2021), 1-4
A. A. Davydov, “Existence of Optimal Stationary States of Exploited Populations with Diffusion”, Proc. Steklov Inst. Math., 310 (2020), 124–130
11.
Differentsialnye uravneniya i dinamicheskie sistemy, Sbornik statei, Trudy MIAN, 308, ed. S. M. Aseev, A. A. Davydov, G. P. Panasenko, MIAN, M., 2020 , 276 pp.
2019
12.
A. A. Davydov, Yu. A. Kasten, “On Structural Stability of Characteristic Nets and the Cauchy Problem for a Tricomi–Cibrario Type Equation”, Proc. Steklov Inst. Math., 304 (2019), 146–152
A. A. Davydov, Y. A. Kasten, “On Nonlocal Normal Forms of Linear Second Order Mixed Type PDEs on the Plane”, Control Systems and Mathematical Methods in Economics., Lecture Notes in Economics and Mathematical Systems, 687, eds. Feichtinger G., Kovacevic R., Tragler G., Springer, 2018, 15 – 25https://link.springer.com/chapter/10.1007/978-3-319-75169-6_2#citeas
15.
T. Manzoor, E. Rovenskaya, A. Davydov, A. Muhammad, “Learning Through Fictitious Play in a Game-Theoretic Model of Natural Resource Consumption”, IEEE Control Systems Letters, 2:1 (2018), 163 – 168
A. Davydov, “Normal forms of linear second order partial differential equations on the plane.”, Sci China Math, 61 (2018), 1-16 (to appear) https://doi.org/10.1007/s11425-017-9303-0
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
2015
19.
A. A. Davydov, A. F. Nassar, “On the Uniqueness of a Positive Stationary State in the Dynamics of a Population with Asymmetric Competition”, Proc. Steklov Inst. Math., 291 (2015), 78–86
20.
A. O. Belyakov, A. A. Davydov, V. M. Veliov, “Optimal Cyclic Exploitation of Renewable Resources”, Journal of Dynamical and Control Systems, 21:3 (2015), 475 – 494
A. A. Davydov, A. F. Nassar, “Stationary Regime of Exploitation of Size-Structured Population with Hierarchical Competition”, Journal of Mathematical Sciences, 205:2 (2015), 199 – 204
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, “Dmitrii Viktorovich Anosov (obituary)”, Russian Math. Surveys, 70:2 (2015), 369–381
2014
23.
A. A. Davydov, A. F. Nassar, “On a stationary state in the dynamics of a population with hierarchical competition”, Russian Math. Surveys, 69:6 (2014), 1126–1128
24.
A. A. Davydov, V. V. Kozlov, F. L. Chernous'ko, “International mathematical conferences and schools for young researchers in Suzdal'”, Russian Math. Surveys, 69:1 (2014), 183–185
25.
A. A. Davydov, A. S. Platov, “Optimal exploitation of two competing size-structured populations”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 49–54
2013
26.
A. A. Davydov, T. S. Shutkina, “Generic Profit Singularities of One-Parameter Cyclic Processes with Discount”, J. Math. Sci, 195:3 (2013), 288 – 298
2014
27.
A. A. Davydov, A. S. Platov, “Optimal stationary solution for a model of exploitation of a population under intraspecific competition”, Journal of Mathematical Sciences, 201:6 (2014), 746–750
2012
28.
A. A. Davydov, A. S. Platov, “Optimal stationary solution in forest management model by accounting intra-species competition”, Mosc. Math. J., 12:2 (2012), 269–273
A. A. Davydov, V. M. Zakalyukin, “Controllability of non-linear systems: generic singularities and their stability”, Russian Math. Surveys, 67:2 (2012), 255–280
30.
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, “Vladimir Mikhailovich Zakalyukin (obituary)”, Russian Math. Surveys, 67:2 (2012), 375–379
2014
31.
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
2012
32.
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
2011
33.
A. A. Davydov, A. S. Platov, “Optimization of stationary solution of a model of size-structured population exploitation”, J. Math.Sci., 176:6 (2011), 860 – 869
A. A. Davydov, T. S. Shutkina, “Time average optimization of cycle process with profit and effort discounts”, Nelin. Dinam., 6:1 (2010), 151–158
35.
A. A. Davydov, L. Trinh Thi Diep, “Normal forms for families of linear equations of mixed type near non-resonant folded singular points”, Russian Math. Surveys, 65:5 (2010), 984–986
36.
A. Davydov, R. Pastres, I. Petrenko, “Optimization of the spatial distribution of pollution emission in 1D flow”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 5, 2010, 30–35
37.
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, “In memory of Evgenii Frolovich Mishchenko”, Proc. Steklov Inst. Math., 271 (2010), 1–2
2009
38.
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
39.
A. A. Davydov, V. I. Danchenko, M. Yu. Zvyagin, “Existence and Uniqueness of a Stationary Distribution of a Biological Community”, Proc. Steklov Inst. Math., 267 (2009), 40–49
2008
40.
A. A. Davydov, M. A. Komarov, “Local Controllability Bifurcations in Families of Bidynamical Systems on the Plane”, Proc. Steklov Inst. Math., 261 (2008), 84–93
41.
A. Davydov, D. Brigolin, R. Pastres, I. Petrenko, “Optimization of shellfish production carrying capacity at a farm scale”, Applied Mathematics and Computations, 204:2 (2008), 532 – 540
A. Davydov, G. Ishikawa, S. Izumiya, W.-Z. Sun, “Generic singularities of implicit systems of first order differential equations on the plane”, Japanese Journal of Mathematics, 3:1 (2008), 93-120
A. A. Davydov, N. B. Melnikov, “Andronov–Hopf bifurcation in simple double diffusion models”, Russian Math. Surveys, 62:2 (2007), 382–384
44.
A. A. Davydov, H. Mena Matos, “Generic phase transitions and profit singularities in Arnol'd's model”, Sb. Math., 198:1 (2007), 17–37
45.
A. A. Davydov, N. B. Melnikov, “Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes”, Proc. Steklov Inst. Math., 259 (2007), 6–15
46.
Yu. A. Grishina, A. A. Davydov, “Structural Stability of Simplest Dynamical Inequalities”, Proc. Steklov Inst. Math., 256 (2007), 80–91
47.
A. A. Davydov, H. Mena-Matos, “Singularity theory approach to time averaged optimization”, SINGULARITIES IN GEOMETRY AND TOPOLOGY, World Scientific Publishing Co. Pte. Ltd., 2007, 598 – 628
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, “Vladimir Igorevich Arnold in the Eyes of His Students: On the occasion of his 70th birthday”, Proc. Steklov Inst. Math., 259 (2007), 1–5
2005
49.
A. A. Davydov, “Generic Profit Singularities in Arnold's Model of Cyclic Processes”, Proc. Steklov Inst. Math., 250 (2005), 70–84
50.
V. I. Arnold, A. A. Davydov, V. A. Vassiliev, V. M. Zakalyukin, “Mathematical models and control of catastrophic processes”, UNESCO Encyclopaedia of Life Support Systems, v. II, eds. V. I. Agoshkov, J.-P. Puel, EOLSS Publishers, Oxford, UK, 2005, 3 – 46http://www.eolss.net/Sample-Chapters/C02/E6-03A-07-05.pdf
2002
51.
A. A. Davydov, “Singularities of Limiting Directions of Generic Higher Order Implicit ODEs”, Proc. Steklov Inst. Math., 236 (2002), 124–131
2001
52.
A. A. Davydov, L. Trinh Thi Diep, “Reduction theorem and normal forms of linear second order mixed type PDE families in the plane”, TWMS Jour. Pure Appl. Math., 2:1 (2001), 44 - 53
53.
A. A. Davydov, L. Trinh Thi Diep, “Reduction theorem and normal forms of linear second order mixed type PDE families in the plane”, TWMS Jour. Pure Appl. Math., 2:1 (2001), 44 - 53
54.
A. Davydov, H. Jongen,, “Normal Forms in One-Parametric Optimization”, Annals of Operations Research, 101 (2001), 255-265https://doi.org/10.1023/A:1010941111726
A. A. Davydov, J. Basto-Gonsalves, “Controllability of Generic Inequalities Near Singular Points.”, Journal of Dynamical and Control Systems, 7 (2001), 77–99
A. A. Davydov, J. Basto-Goncalves, “Controllability of inequalities at 2-singular points”, Russian Math. Surveys, 55:6 (2000), 1139–1140
2001
57.
A. A. Davydov, V. M. Zakalyukin, “The coincidence of generic singularities of solutions of extremal problems with constraints”, J. Math. Sci. (New York), 103:6 (2001), 709–724
1999
58.
A. A. Davydov, V. M. Zakalyukin, “Classification of relative minima singularities”, Banach Center Publication, Geometry and Topolgy of Caustics, 50 (1999), 75 – 90
1998
59.
A. A. Davydov, V. M. Zakalyukin, “Point singularities of a conditional minimum on a three-dimensional manifold”, Proc. Steklov Inst. Math., 220 (1998), 109–125
60.
Aleksey Davydov, “Controllability of generic control systems on surfaces”: B. Jakubczyk, W. Respondek, MONOGRAPHS AND TEXTBOOKS IN PURE AND APPLIED MATHEMATICS, v. 207, MARCEL DEKKEr, INC, ., Geometry of Feedback and Optimal Control, Chapman & Hall/CRC, 1998, 111-164
61.
A. A. Davydov, E. Rosales-Gonzales, “Smooth normal forms of folded resonance saddles and nodes and complete classification of generic linear second order PDE's on the plane,”, Equadiff 95, International Conference on Differential Equations, Lisbon 1995, eds. Magalhaes, L., Rocha, C., Sanchez, L., Singapore: World Scientific, 1998, 59 – 68
1996
62.
A. A. Davydov, È. Rosales-Gonsales, “Complete classification of generic linear second-order partial differential equations in the plane”, Dokl. Akad. Nauk, 350:2 (1996), 151–154
1995
63.
A. A. Davydov, L. Ortiz-Bobadil'ya, “Normal forms of folded elementary singular points”, Russian Math. Surveys, 50:6 (1995), 1260–1261
64.
A. A. Davydov, “Local controllability of typical dynamical inequalities on surfaces”, Proc. Steklov Inst. Math., 209 (1995), 73–106
65.
A. A. Davydov, L. Ortiz-Bobadilla, “Smooth normal forms of folded elementary singular points”, Davydov, A.A. & Ortiz-Bobadilla, L. Journal of Dynamical and Control Systems (1995) 1: 463. https://doi.org/10.1007/BF02255893, Journal of Dynamical and Control Systems, 1:4 (1995), 463 – 482https://link.springer.com/article/10.1007/BF02255893
A. A. Davydov, Qualitative theory of control systems, Translations of Mathematical Monographs, 141, American Mathematical Society, Providence, RI, 1994 , viii+147 pp.
A. A. Davydov, “Structural stability of control systems on orientable surfaces”, Math. USSR-Sb., 72:1 (1992), 1–28
1990
69.
A. A. Davydov, “The quasi-Hölder property of the boundary of attainabilitystatya”, Selecta Mathematica Sovietica, 93 (1990), 229 – 234
1989
70.
A. A. Davydov, “Singularities of fields of limiting directios of two-dimensional control systems”, Math. USSR-Sb., 64:2 (1989), 471–493
1988
71.
A. A. Davydov, “The normal form of slow motions of an equation of relaxation type and fibrations of binomial surfaces”, Math. USSR-Sb., 60:1 (1988), 133–141
1985
72.
A. A. Davydov, “Normal form of a differential equation, not solvable for the derivative, in a neighborhood of a singular point”, Funct. Anal. Appl., 19:2 (1985), 81–89
73.
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, “Sessions of the Petrovskii seminar on differential equations and mathemathical problems of physics”, Uspekhi Mat. Nauk, 40:5(245) (1985), 295–307
1982
74.
A. A. Davydov, “Singularities of the admissibility boundary in two-dimensional control systems”, Russian Math. Surveys, 37:3 (1982), 200–201
On optimal stationary conditions of exploited populations A. A. Davydov International Conference "Classical Mechanics, Dynamical Systems and Mathematical Physics" on the occasion of V. V. Kozlov 70th birthday January 24, 2020 15:45
9.
Stability of controllability of dynamic inequalities A. A. Davydov International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin December 14, 2018 09:00
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
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
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
Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 308, ed. S. M. Aseev, A. A. Davydov, G. P. Panasenko, 2020, 276 с. http://mi.mathnet.ru/book1782
2024
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