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Rodina, Lyudmila Ivanovna
Statistics Math-Net.Ru
Total publications: 57
Scientific articles: 50
Talks: 6

Number of views:
This page:4504
Abstract pages:32563
Full texts:14455
Talk pages:2328
Video records:129
Rodina, Lyudmila Ivanovna
Associate professor
Doctor of physico-mathematical sciences (2012)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail: ;
Keywords: Control systems, dynamical systems, control theory, the theory of invariance or viability.
UDC: 517.977, 517.911, 517.93, 517.935, 517.938
MSC: 34A60, 37N35, 49J15, 93B03

Subject:

Mathematic control theory. Dynamical systems. The stability theory of control systems. The control systems with randon coefficients.
   
Main publications:
  1. L.I. Rodina, “Prostranstvo $slsv(R^n)$ s metrikoi Khausdorfa–Bebutova i statisticheski invariantnye mnozhestva upravlyaemykh sistem”, Trudy MIAN, 278 (2012), 217–226
  2. L.I. Rodina, “Invariantnye i statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Izv. IMI UdGU, 2012, № 2(40), 3–164
  3. L.I. Rodina, “Statisticheski invariantnye mnozhestva upravlyaemykh sistem so sluchainymi parametrami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki., 2011, № 2, 68–87
  4. L.I. Rodina, E.L. Tonkov, “Statisticheskie kharakteristiki mnozhestva dostizhimosti upravlyaemoi sistemy, nebluzhdaemost i minimalnyi tsentr prityazheniya”, Nelineinaya dinamika, 5:2 (2009), 265–288
  5. E.A. Panasenko, L.I. Rodina, E.L. Tonkov, “Prostranstvo $clcv(R^n)$ s metrikoi Khausdorfa–Bebutova i differentsialnye vklyucheniya”, Trudy IMM UrO RAN, 17:1 (2011), 162–177

https://www.mathnet.ru/eng/person44330
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/758399
https://orcid.org/0000-0003-1077-2189

Publications in Math-Net.Ru Citations
2025
1. L. I. Rodina, A. H. Hammady, A. V. Chernikova, “Problems of optimal periodic resource harvesting for population models described by difference equations”, Russian Universities Reports. Mathematics, 30:151 (2025),  255–266  mathnet
2. L. I. Rodina, “Estimates of harvesting characteristicsfor stochastic structured populations”, Russian Universities Reports. Mathematics, 30:149 (2025),  66–78  mathnet
2024
3. A. A. Bazulkina, L. I. Rodina, “Comparison theorem for systems of differential equations and its application to estimate the average time benefit from resource collection”, Izv. IMI UdGU, 63 (2024),  3–17  mathnet 1
4. L. I. Rodina, “On some classes of systems of differential equations”, Russian Universities Reports. Mathematics, 29:145 (2024),  77–85  mathnet 1
2023
5. M. S. Woldeab, L. I. Rodina, “On the exploitation of a population given by a system of linear equations with random parameters”, Izv. IMI UdGU, 61 (2023),  27–41  mathnet
6. L. I. Rodina, A. V. Chernikova, “On infinite-horizon optimal exploitation of a renewable resource”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:1 (2023),  167–179  mathnet  mathscinet  elib 2
2022
7. M. S. Woldeab, L. I. Rodina, “About the methods of biological resourse extraction, that provide the maximum average time benefit”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 1,  12–24  mathnet  mathscinet; Russian Math. (Iz. VUZ), 66:1 (2022), 8–18 4
8. M. S. Woldeab, L. I. Rodina, “About the methods of renewable resourse extraction from the structured population”, Russian Universities Reports. Mathematics, 27:137 (2022),  16–26  mathnet 4
9. A. A. Rodin, L. I. Rodina, A. V. Chernikova, “On how to exploit a population given by a difference equation with random parameters”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:2 (2022),  211–227  mathnet  mathscinet 3
2021
10. L. I. Rodina, “Profit maximization problems in various economic models”, Math. Ed., 2021, no. 2(98),  44–49  mathnet
2020
11. Yu. V. Masterkov, L. I. Rodina, “Estimation of average time profit for stochastic structured population”, Izv. IMI UdGU, 56 (2020),  41–49  mathnet 4
2019
12. A. V. Egorova, L. I. Rodina, “On optimal harvesting of renewable resource from the structured population”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019),  501–517  mathnet 9
2018
13. L. I. Rodina, I. I. Tyuteev, “On estimation of an average time profit in probabilistic environmental and economic models”, Model. Anal. Inform. Sist., 25:3 (2018),  257–267  mathnet  elib 2
14. L. I. Rodina, “On asymptotic properties of solutions of control systems with random parameters”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:1 (2018),  189–199  mathnet  elib; Proc. Steklov Inst. Math., 304: suppl. 1 (2019), S144–S153  isi  scopus
15. L. I. Rodina, “About one stochastic harvesting model of a renewed resourse”, Tambov University Reports. Series: Natural and Technical Sciences, 23:124 (2018),  685–695  mathnet  elib 3
16. L. I. Rodina, “Properties of average time profit in stochastic models of harvesting a renewable resource”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:2 (2018),  213–221  mathnet  elib 12
17. L. I. Rodina, “Optimization of average time profit for a probability model of the population subject to a craft”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018),  48–58  mathnet  elib 19
2017
18. L. I. Rodina, “On the stability of a linear system of difference equations with random parameters”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132 (2017),  105–108  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 230:5 (2018), 757–761  scopus
19. Ya. Yu. Larina, L. I. Rodina, “Extension of the concept of invariance and statistically weakly invariant sets of controllable systems”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132 (2017),  57–60  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 230:5 (2018), 703–707  scopus
20. Ya. Yu. Larina, L. I. Rodina, “Statistical characteristics of continuous functions and statistically weakly invariant sets of controllable system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 2,  34–43  mathnet; Russian Math. (Iz. VUZ), 61:2 (2017), 28–35  isi  scopus
21. L. I. Rodina, A. H. Hammady, “On the invariant sets and chaotic solutions of difference equations with random parameters”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:2 (2017),  238–247  mathnet  elib
2016
22. L. I. Rodina, A. H. Hammady, “Characteristics of invariancy for the attainability set of a control system”, Izv. IMI UdGU, 2016, no. 1(47),  44–53  mathnet  elib
23. L. I. Rodina, “On repelling cycles and chaotic solutions of difference equations with random parameters”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  227–235  mathnet  mathscinet  elib 3
24. Ya. Yu. Larina, L. I. Rodina, “Asymptotically stable sets of control systems with impulse actions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:4 (2016),  490–502  mathnet  mathscinet  elib 3
25. L. I. Rodina, I. I. Tyuteev, “About asymptotical properties of solutions of difference equations with random parameters”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016),  79–86  mathnet  mathscinet  elib 9
2014
26. L. I. Rodina, A. Kh. Khammadi, “Statistical characteristics of attainability set of controllable systems with random coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 11,  50–63  mathnet; Russian Math. (Iz. VUZ), 58:11 (2014), 43–53  scopus 6
27. L. I. Rodina, “On the invariant sets of control systems with random coefficients”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4,  109–121  mathnet 4
2013
28. L. I. Rodina, “Estimation of statistical characteristics of attainability sets of controllable systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 11,  20–32  mathnet; Russian Math. (Iz. VUZ), 57:11 (2013), 17–27  scopus 10
29. Y. Y. Larina, L. I. Rodina, “Statistical Characteristics of Control Systems, Arising in Various Models of Natural Sciences”, Model. Anal. Inform. Sist., 20:5 (2013),  62–77  mathnet 1
30. L. I. Rodina, “On some probability models of dynamics of population growth”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4,  109–124  mathnet 5
31. L. I. Rodina, A. H. Hammady, “The characteristics of attainability set connected with invariancy of control systems on the finite time interval”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 1,  35–48  mathnet 2
2012
32. L. I. Rodina, “Invariant and statistically weakly invariant sets of control systems”, Izv. IMI UdGU, 2012, no. 2(40),  3–164  mathnet 12
33. L. I. Rodina, “Statistical characteristics of attainable set of controllable systems”, Izv. IMI UdGU, 2012, no. 1(39),  111–113  mathnet
34. L. I. Rodina, “The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff–Bebutov metric and statistically invariant sets of control systems”, Trudy Mat. Inst. Steklova, 278 (2012),  217–226  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 278 (2012), 208–217  isi  elib  scopus 5
35. L. I. Rodina, E. L. Tonkov, “About the attainability set of control system without assumption of compactness of geometrical restrictions on admissible controls”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 4,  68–79  mathnet 1
36. L. I. Rodina, “Statistical characteristics of attainability set and periodic processes of control systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 2,  34–43  mathnet 4
2011
37. E. A. Panasenko, L. I. Rodina, E. L. Tonkov, “The space $\mathrm{clcv}(\mathbb R^n)$ with the Hausdorff–Bebutov metric and differential inclusions”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:1 (2011),  162–177  mathnet  elib; Proc. Steklov Inst. Math., 275: suppl. 1 (2011), S121–S136  isi  scopus 14
38. L. I. Rodina, “The statistically invariant sets of controllable systems with random parameters”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 2,  68–87  mathnet 5
39. L. I. Rodina, E. L. Tonkov, “The statistically weak invariant sets of control systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 1,  67–86  mathnet 13
2010
40. E. A. Panasenko, L. I. Rodina, E. L. Tonkov, “Asymptotically stable statistically weakly invariant sets for controlled systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010),  135–142  mathnet  elib 7
2009
41. L. I. Rodina, E. L. Tonkov, “Statistical characteristics of attainable set of controllable system, non-wandering, and minimal attraction center”, Nelin. Dinam., 5:2 (2009),  265–288  mathnet 23
2008
42. Yu. V. Masterkov, L. I. Rodina, “Sufficient conditions for the local controllability of systems with random parameters for an arbitrary number of states of a system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 3,  38–49  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 52:3 (2008), 34–44 7
43. E. A. Panasenko, L. I. Rodina, E. L. Tonkov, “Absorption, nonwandering, and reccurence of the attainable set of a controllable system”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 2,  97–104  mathnet 4
2006
44. L. I. Rodina, “Conditions for existence of nonanticipating control function for systems with random parameters”, Izv. IMI UdGU, 2006, no. 3(37),  131–132  mathnet 1
45. L. I. Rodina, “The construction of the non-predicting control for systems with random parameters”, Izv. IMI UdGU, 2006, no. 2(36),  95–98  mathnet 1
46. Ju. V. Masterkov, L. I. Rodina, “The conditions of local controllability for linear systems with stochastic parameters”, Vestn. Udmurtsk. Univ. Mat., 2006, no. 1,  81–94  mathnet 2
2005
47. Ju. V. Masterkov, L. I. Rodina, “The construction of non-anticipatory control for linear systems with stochastic parameters”, Vestn. Udmurtsk. Univ. Mat., 2005, no. 1,  101–114  mathnet 2
2004
48. Yu. V. Masterkov, L. I. Rodina, “Sufficient Conditions for the Stable Controllability of a Nonautonomous System in the Critical Case”, Differ. Uravn., 40:1 (2004),  33–40  mathnet  mathscinet; Differ. Equ., 40:1 (2004), 33–42 1
2003
49. Yu. V. Masterkov, L. I. Rodina, “Sufficient and Necessary Conditions for the Stable Controllability of a Nonlinear Nonstationary System on the Plane in the Critical Case”, Differ. Uravn., 39:2 (2003),  227–235  mathnet  mathscinet; Differ. Equ., 39:2 (2003), 246–255 1
2002
50. L. I. Rodina, E. L. Tonkov, “The criterion of complete controllability of linear time-varying system in the critical case”, Izv. IMI UdGU, 2002, no. 2(25),  81–86  mathnet 1
2024
51. L. I. Rodina, A. V. Chernikova, “On the properties of systems of differential equations and problems of optimal resource extraction”, Math. Ed., 2024, no. 3(111),  31–45  mathnet
2019
52. A. A. Gryzlov, V. A. Zaitsev, D. M. Kinzebulatov, N. V. Latypova, V. P. Maksimov, N. N. Petrov, S. N. Popova, V. I. Rodionov, L. I. Rodina, Yu. M. Smetanin, D. L. Fedorov, “Vasilii Yakovlevich Derr. To anniversary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019),  612–617  mathnet
2015
53. A. A. Gryzlov, V. Ya. Derr, V. A. Zaitsev, A. I. Karpov, I. V. Men'shikov, N. N. Petrov, L. I. Rodina, “Svetlana Nikolaevna Popova. To anniversary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:4 (2015),  596–600  mathnet  elib
54. N. N. Petrov, S. P. Blinov, L. I. Rodina, V. Ya. Derr, “Lev Isaakovich Tuchinskii. To anniversary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:4 (2015),  593–595  mathnet  elib
2014
55. I. V. Gaishun, A. A. Gryzlov, V. Ya. Derr, N. A. Izobov, A. I. Karpov, E. K. Makarov, G. V. Merzlyakova, N. N. Petrov, S. N. Popova, L. I. Rodina, N. Kh. Rozov, I. N. Sergeev, A. A. Tolstonogov, V. N. Ushakov, A. G. Chentsov, “In memory of Evgenii Leonidovich Tonkov (27.06.1940–28.09.2014)”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4,  146–154  mathnet
56. A. A. Gryzlov, A. I. Karpov, N. V. Latypova, N. N. Petrov, L. I. Rodina, D. L. Fedorov, “Vasilii Yakovlevich Derr. A tribute in honor of his seventy-fifth birthday”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4,  142–145  mathnet
2013
57. A. V. Borisov, A. A. Gryzlov, V. Ya. Derr, A. I. Karpov, N. V. Latypova, L. I. Rodina, E. L. Tonkov, V. N. Ushakov, “Petrov Nikolai Nikandrovich (on his sixties birthday)”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4,  175–180  mathnet

Presentations in Math-Net.Ru
1. On the properties of systems of differential equations and problems of optimal resource extraction
L. I. Rodina
Seminar on mathematical modeling in biology and medicine
October 3, 2024 16:30
2. Comparison Theorems for Systems of Differential Equations and Their Application to Solving Applied Problems.
L. I. Rodina
Geometric Theory of Optimal Control
April 4, 2024 16:45   
3. On the property of monotonicity of solutions of systems with respect to initial conditions
L. I. Rodina
III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov
July 10, 2023 12:45   
4. On optimal resource harvesting in a structured population
M. S. Woldeab, L. I. Rodina
International Conference “Differential Equations and Optimal Control” dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko
June 9, 2022 12:50   
5. About extension of consept of invariancy for sets concerning control systems
Ya. Yu. Larina, L. I. Rodina
International Conference on Mathematical Control Theory and Mechanics
July 4, 2015 11:40
6. Conditions of invariancy and extinction for probability model of population dynamics
L. I. Rodina
International Conference on Differential Equations and Dynamical Systems
July 8, 2014 15:00

Organisations
 
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