Davydov, Alexey Alexandrovich

Total publications: 60 (52)
in MathSciNet: 49 (44)
in zbMATH: 39 (36)
in Web of Science: 25 (21)
in Scopus: 30 (28)
Cited articles: 36
Citations in Math-Net.Ru: 138
Citations in Web of Science: 63
Citations in Scopus: 69
Presentations: 14

Number of views:
This page:8414
Abstract pages:18366
Full texts:4748
Doctor of physico-mathematical sciences (1993)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 20.09.1956
Phone: +7 (495) 939 43 89
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


Singularity theory, differential equation, mathematical control theory.


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
List of publications on Google Scholar
List of publications on ZentralBlatt

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |

1. A. A. Davydov, Избранные вопросы математики и механики, Tr. Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020 (to appear)  mathnet

2. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus

3. 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 – 25  crossref  mathscinet  zmath  isi  scopus
4. 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  crossref  mathscinet  scopus (cited: 4)
5. A. Davydov, “Normal forms of linear second order partial differential equations on the plane.”, Sci China Math, 61 (2018), 1-16 (to appear)  crossref  mathscinet  isi (cited: 3)  scopus (cited: 3)

6. A. O. Belyakov, A. A. Davydov, V. M. Veliov, “Optimal Cyclic Harvesting of Renewable Resource1”, Doklady Mathematics, 96:2 (2017), 472 – 474  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus
7. 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 (cited: 1)  elib  scopus (cited: 1)

8. 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  mathnet  crossref  crossref  isi  elib  elib  scopus
9. 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  crossref  mathscinet  zmath  scopus (cited: 8)
10. 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 (to appear)  crossref  mathscinet  zmath  scopus (cited: 1)

11. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib  elib  scopus
12. 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  mathnet  crossref  mathscinet  isi  elib  scopus

13. A. A. Davydov, T. S. Shutkina, “Generic Profit Singularities of One-Parameter Cyclic Processes with Discount”, J. Math. Sci, 195:3 (2013), 288 – 298  crossref  mathscinet  zmath  elib  scopus

14. 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  mathnet  crossref  scopus

15. 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  mathnet (cited: 6)  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 8)
16. A. A. Davydov, V. M. Zakalyukin, “Controllability of non-linear systems: generic singularities and their stability”, Russian Math. Surveys, 67:2 (2012), 255–280  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib  elib  scopus (cited: 2)

17. 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  scopus (cited: 1)

18. 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  scopus

19. 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  crossref  mathscinet  zmath  elib  scopus (cited: 3)

20. A. A. Davydov, T. S. Shutkina, “Time average optimization of cycle process with profit and effort discounts”, Nelin. Dinam., 6:1 (2010), 151–158  mathnet  elib
21. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 3)
22. 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  mathnet  elib

23. 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 (cited: 2)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 3)
24. 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  mathnet  crossref  mathscinet  zmath  isi (cited: 5)  elib  elib  scopus (cited: 4)

25. 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  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
26. 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  crossref  mathscinet  zmath  scopus (cited: 8)
27. 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  crossref  mathscinet  scopus (cited: 15)

28. A. A. Davydov, N. B. Melnikov, “Andronov–Hopf bifurcation in simple double diffusion models”, Russian Math. Surveys, 62:2 (2007), 382–384  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
29. 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 (cited: 5)  elib (cited: 5)  elib (cited: 5)  scopus (cited: 7)
30. 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  mathnet  crossref  mathscinet  zmath  elib  elib  scopus
31. Yu. A. Grishina, A. A. Davydov, “Structural Stability of Simplest Dynamical Inequalities”, Proc. Steklov Inst. Math., 256 (2007), 80–91  mathnet  crossref  mathscinet  zmath  elib (cited: 1)  elib (cited: 1)  scopus (cited: 5)
32. 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  crossref  mathscinet  zmath

33. A. A. Davydov, “Generic Profit Singularities in Arnold's Model of Cyclic Processes”, Proc. Steklov Inst. Math., 250 (2005), 70–84  mathnet  mathscinet  zmath
34. 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 – 46

35. A. A. Davydov, “Singularities of Limiting Directions of Generic Higher Order Implicit ODEs”, Proc. Steklov Inst. Math., 236 (2002), 124–131  mathnet  mathscinet  zmath

36. 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  mathscinet
37. 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  mathscinet

38. A. A. Davydov, J. Basto-Goncalves, “Controllability of inequalities at 2-singular points”, Russian Math. Surveys, 55:6 (2000), 1139–1140  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  scopus

39. 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  mathnet  crossref  mathscinet  zmath

40. 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  mathnet  mathscinet  zmath
41. 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  mathscinet

42. 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  mathnet  mathscinet  zmath

43. A. A. Davydov, L. Ortiz-Bobadil'ya, “Normal forms of folded elementary singular points”, Russian Math. Surveys, 50:6 (1995), 1260–1261  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)
44. A. A. Davydov, “Local controllability of typical dynamical inequalities on surfaces”, Proc. Steklov Inst. Math., 209 (1995), 73–106  mathnet  mathscinet  zmath
45. 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., Journal of Dynamical and Control Systems, 1:4 (1995), 463 – 482  crossref  mathscinet  zmath
46. Aleksey Davydov, “Singularities of the maximum function over a preimage”, DOI: 10.4064/-32-1-167-181, Banach Center Publications, 32, Institute of Mathematics of Polish Academy of Sciences, 1995, 167 – 181  crossref  mathscinet  zmath

47. A. A. Davydov, Qualitative theory of control systems, Translations of Mathematical Monographs, 141, American Mathematical Society, Providence, RI, 1994 , viii+147 pp.  crossref  mathscinet  zmath

48. A. A. Davydov, “Structural stability of control systems on orientable surfaces”, Math. USSR-Sb., 72:1 (1992), 1–28  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 5)

49. A. A. Davydov, “Singularities of fields of limiting directios of two-dimensional control systems”, Math. USSR-Sb., 64:2 (1989), 471–493  mathnet  crossref  mathscinet  zmath

50. 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  mathnet  crossref  mathscinet  zmath

51. 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  mathnet  crossref  mathscinet  zmath  isi (cited: 26)

52. A. A. Davydov, “Singularities of the admissibility boundary in two-dimensional control systems”, Russian Math. Surveys, 37:3 (1982), 200–201  mathnet  crossref  mathscinet  zmath  adsnasa

Presentations in Math-Net.Ru
1. 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   
2. 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   
3. 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   
4. 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   
5. 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   
6. 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   
7. К теории нормальных форм уравнений смешанного типа на плоскости
A. A. Davydov
Dynamical systems and differential equations
May 22, 2017 18:30
8. 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   
9. 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   
10. Особенности оптимизации циклических процессов
A. A. Davydov
Steklov Mathematical Institute Seminar
February 18, 2016 16:00   
11. 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
12. 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
13. 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   
14. 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   

Books in Math-Net.Ru
  1. Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 308, ed. S. M. Aseev, A. A. Davydov, G. P. Panasenko, 2020, 276 с.

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