05.13.18; 05.13.17 (Mathematical modeling, numerical methods, and the program systems; Theoretical foundation for informatics)
Keywords:
Differential equations with small parameters, branching theory, stability with respect to a part of variables, parameter identification.
Subject:
differential equations in Banach spaces with small parameters, methods of branching theory and their applications in the theory of oscillations and wave equations, local reducibility and asymptotic equivalence of nonlinear ODE systems, stability with respect to a part of variables, mathematical models of physics, mechanics, chemical kinetics, biology, identification of dynamic system parameters from experimental data.
Main publications:
A. A. Kyashkin, B. V. Loginov, P. A. Shamanaev, “O vetvlenii periodicheskikh reshenii lineinykh neodnorodnykh differentsialnykh uravnenii c vyrozhdennym ili tozhdestvennym operatorom pri proizvodnoi i vozmuscheniem v vide malogo lineinogo slagaemogo”, Zhurnal Srednevolzhskogo matematicheskogo obschestva, 18:1 (2016), 45–53
P. A. Shamanaev, “On the partial instability of the zero solution of nonlinear systems to the first approximation”, Zhurnal SVMO, 26:3 (2024), 280–293
2023
2.
E. V. Desyaev, P. A. Shamanaev, “On periodic solutions of linear inhomogeneous differential equations with a small perturbation at the derivative”, Zhurnal SVMO, 25:3 (2023), 111–122
3.
P. A. Shamanaev, “On the stability of the zero solution with respect to a part of variables in linear approximation”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 19:3 (2023), 374–390
A. A. Kosov, A. V. Shchennikov, E. V. Shchennikova, R. V. Zhalnin, P. A. Shamanaev, “Review of the works of V. N. Shchennikova on the study of the convergence of nonlinear almost periodic systems by the comparison method”, Zhurnal SVMO, 21:2 (2019), 175–186
2018
5.
P. A. Shamanaev, O. S. Yazovtseva, “The sufficient conditions for polystability of solutions of nonlinear systems of ordinary differential equations”, Zhurnal SVMO, 20:3 (2018), 304–317
2017
6.
P. A. Shamanaev, O. S. Yazovtseva, “The sufficient conditions of local asymptotic equivalence of nonlinear systems of ordinary differential equations and its application for investigation of stability respect to part of variables”, Zhurnal SVMO, 19:1 (2017), 102–115
P. A. Shamanaev, B. V. Loginov, “The branching of periodic solutions of inhomogeneous linear differential equations with a the perturbation in the form of small linear term with delay”, Zhurnal SVMO, 18:3 (2016), 61–69
A. A. kjashkin, B. V. Loginov, P. A. Shamanaev, “The branching of periodic solutions of inhomogeneous linear differential equations with degenerate or identity operator in the derivative and the disturbance in the form of small linear term”, Zhurnal SVMO, 18:1 (2016), 45–53
V. K. Ionychev, R. R. Kaderkaev, S. M. Muryumin, P. A. Shamanaev, “Numerical modelling of probability of inclusion of microplasma c participation of the deep centers in $p$–$n$–junction”, Zhurnal SVMO, 17:4 (2015), 78–86
10.
P. A. Shamanaev, “On a class of locally reducible nonlinear systems of ordinary differential equations with perturbations in the form of homogeneous vector polynomials”, Zhurnal SVMO, 17:3 (2015), 56–65
2014
11.
A. A. kjashkin, B. V. Loginov, P. A. Shamanaev, “Comments to the problem on branching of periodical solutions at Andronov-Hopf bifurcation in differential equations with degenerated operator before the derivative”, Zhurnal SVMO, 16:4 (2014), 33–40
V. A. Atryakhin, P. A. Shamanaev, “Application of a system of differential equations with a dvergent argument in modeling a process of scientific staff reproduction”, University proceedings. Volga region. Physical and mathematical sciences, 2013, no. 1, 82–90
13.
A. A. kjashkin, B. V. Loginov, P. A. Shamanaev, “Comments to the problems of small perturbations of linear
equations and linear term of the spectral characteristics of a Fredholm
operator”, Zhurnal SVMO, 15:3 (2013), 100–107
E. E. Peskova, P. A. Shamanaev, “On the construction WENO schemes for hyperbolic systems on triangular meshes”, Zhurnal SVMO, 15:1 (2013), 121–124
2012
15.
V. A. Atryakhin, P. A. Shamanaev, “On the use of
systems of differential equations with delay in predicting the dynamics of socio-economic processes”, Zhurnal SVMO, 14:3 (2012), 29–37
16.
V. A. Atryakhin, P. A. Shamanaev, “Modeling the dynamics of personnel with the use of differential equations with deviating argument”, Zhurnal SVMO, 14:1 (2012), 53–58
V. A. Atryakhin, P. A. Shamanaev, “Building of mathematical models of the dynamics stream
of applicants for graduate school with system of differential
equations with delay”, Zhurnal SVMO, 13:4 (2011), 35–39
P. A. Shamanaev, V. A. Atryakhin, “Numerical simulation of flow dynamics scientific and
teaching staff on the basis of statistical Data on Mordovian State
University after N. P. Ogarev”, Zhurnal SVMO, 13:1 (2011), 84–90
P. A. Shamanaev, V. A. Atryakhin, “Construct a mathematical model forecasting the flow of scientific and scientific-pedagogical staff”, Zhurnal SVMO, 12:4 (2010), 234–238
2009
20.
P. A. Shamanaev, “Sufficient conditions reducibility of differential equations system with perturbations of the higher orders to the linear systems with a constant matrix”, Trudy SVMO, 11:2 (2009), 145–151
2008
21.
P. A. Shamanaev, “On local reducibility of differential equations system with perturbations of the higher orders to the linear systems with a zero matrix”, Trudy SVMO, 10:2 (2008), 213–217
1995
22.
P. A. Shamanaev, “Asymptotic methods of stabilization of programmed motion”, Matem. Mod., 7:5 (1995), 80
2021
23.
O. V. Anashkin, P. M. Akhmet'ev, D. V. Balandin, M. K. Barinova, I. V. Boykov, A. N. Bezdenezhnyh, V. N. Belykh, P. A. Vel'misov, I. Yu. Vlasenko, O. E. Galkin, S. Yu. Galkina, V. K. Gorbunov, S. D. Glyzin, S. V. Gonchenko, A. S. Gorodetski, E. V. Gubina, E. Ya. Gurevich, A. A. Davydov, L. S. Efremova, R. V. Zhalnin, A. Yu. Zhirov, E. V. Zhuzhoma, N. I. Zhukova, S. Kh. Zinina, Yu. S. Ilyashenko, N. V. Isaenkova, A. O. Kazakov, A. V. Klimenko, S. A. Komech, Yu. A. Kordyukov, V. E. Kruglov, E. V. Kruglov, E. B. Kuznetsov, S. K. Lando, Yu. A. Levchenko, L. M. Lerman, S. I. Maksimenko, M. I. Malkin, D. S. Malyshev, V. K. Mamaev, T. Ph. Mamedova, V. S. Medvedev, T. V. Medvedev, D. I. Mints, T. M. Mitryakova, A. D. Morozov, A. I. Morozov, E. V. Nozdrinova, E. N. Pelinovsky, Ya. B. Pesin, A. S. Pikovsky, S. Yu. Pilyugin, G. M. Polotovsky, O. V. Pochinka, I. D. Remizov, P. E. Ryabov, A. S. Skripchenko, A. V. Slunyaev, S. V. Sokolov, L. A. Sukharev, E. A. Talanova, V. A. Timorin, S. B. Tikhomirov, V. F. Tishkin, D. V. Treschev, D. V. Turaev, N. G. Chebochko, E. E. Chilina, P. A. Shamanaev, D. D. Shubin, E. I. Yakovlev, “To the 75th anniversary of Vyacheslav Zigmundovich Grines”, Zhurnal SVMO, 23:4 (2021), 472–476
24.
P. A. Vel'misov, V. Z. Grines, R. V. Zhalnin, E. B. Kuznetsov, T. Ph. Mamedova, P. V. Senin, L. A. Sukharev, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, O. S. Yazovtseva, “To the 80th anniverssry of Ilya Vladimirovich Boykov”, Zhurnal SVMO, 23:3 (2021), 318–321
25.
A. S. Andreev, I. V. Boykov, P. A. Vel'misov, V. Z. Grines, E. V. Desyaev, D. K. Egorova, R. V. Zhalnin, E. B. Kuznetsov, I. V. Lutoshkin, A. G. Lvov, T. Ph. Mamedova, S. M. Muryumin, I. P. Ryazantseva, P. V. Senin, D. N. Sidorov, N. A. Sidorov, L. A. Sukharev, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, “To the 80th anniversary of Vladimir Konstantinovich Gorbunov”, Zhurnal SVMO, 23:2 (2021), 207–210
26.
V. V. Abramov, D. I. Boyarkin, I. M. Burkin, K. V. Bukhensky, O. V. Druzhinina, D. K. Egorova, R. V. Zhalnin, I. V. Ionova, A. N. Konenkov, A. N. Kulikov, A. G. Kushner, E. Yu. Liskina, S. S. Mamonov, O. N. Masina, A. K. Murtazov, A. Yu. Pavlov, P. M. Simonov, A. O. Harlamova, T. Ph. Mamedova, S. M. Muryumin, V. I. Safonkin, G. A. Smolkin, L. A. Sukharev, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, “In memory of Terekhin Mihail Tihonovich”, Zhurnal SVMO, 23:1 (2021), 110–111
2020
27.
I. V. Boykov, P. A. Vel'misov, È. R. Gizzatova, V. K. Gorbunov, V. Z. Grines, I. M. Gubaydullin, Yu. N. Deryugin, E. V. Desyaev, D. K. Egorova, A. P. Zhabko, R. V. Zhalnin, A. S. Ismagilova, V. N. Krizsky, E. B. Kuznetsov, T. Ph. Mamedova, N. D. Morozkin, S. M. Muryumin, S. A. Mustafina, O. V. Pochinka, I. P. Ryazantseva, K. B. Sabitov, L. A. Sukharev, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, “In memory of Spivak Semen Izrailevich”, Zhurnal SVMO, 22:4 (2020), 463–466
2019
28.
A. Yu. Aleksandrov, L. A. Antoshkina, E. V. Afinogentova, A. S. Andreev, I. G. Bashmakov, P. A. Vel'misov, V. Z. Grines, E. V. Desyaev, O. V. Druzhinina, D. K. Egorova, A. P. Zhabko, R. V. Zhalnin, E. A. Lizina, A. M. Kamachkin, A. A. Kosov, O. G. Kostrov, E. B. Kuznetsov, T. Ph. Mamedova, S. I. Martynov, S. M. Muryumin, V. I. Nikonov, S. I. Peregudin, E. E. Peskova, I. P. Ryazantseva, P. V. Senin, G. A. Smolkin, A. G. Smolyanov, L. A. Sukharev, A. O. Syromyasov, V. F. Tishkin, A. Yu. Uteshev, S. E. Kholodova, I. I. Chuchaev, P. A. Shamanaev, A. V. Shchennikov, E. V. Shchennikova, O. S. Yazovtseva, “In memory of Vladimir Nikolaevich Shchennikov”, Zhurnal SVMO, 21:2 (2019), 269–273
29.
V. V. Abramov, D. I. Boyarkin, I. M. Burkin, K. V. Bukhensky, O. V. Druzhinina, D. K. Egorova, R. V. Zhalnin, I. V. Ionova, A. N. Konenkov, A. N. Kulikov, A. G. Kushner, E. Yu. Liskina, S. S. Mamonov, O. N. Masina, A. K. Murtazov, A. Yu. Pavlov, P. M. Simonov, A. O. Kharlamova, T. Ph. Mamedova, S. M. Muryumin, V. I. Safonkin, G. A. Smolkin, L. A. Sukharev, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, “To the eighty-fifth anniversary of Mikhail Tikhonovich Terekhin”, Zhurnal SVMO, 21:1 (2019), 114–115
30.
I. V. Boykov, D. I. Boyarkin, S. M. Vdovin, P. A. Vel'misov, V. Z. Grines, I. M. Gubaydullin, Yu. N. Deryugin, D. K. Egorova, R. V. Zhalnin, V. T. Zhukov, T. Sh. Kal'menov, L. V. Klochkova, M. M. Krasnov, V. N. Krizsky, E. B. Kuznetsov, M. E. Ladonkina, T. Ph. Mamedova, V. F. Masyagin, P. P. Matus, N. D. Morozkin, S. M. Muryumin, O. A. Neklyudova, Yu. N. Orlov, A. Yu. Pavlov, E. E. Peskova, Yu. A. Poveschenko, I. P. Ryazantseva, V. I. Safonkin, P. V. Senin, G. A. Smolkin, S. I. Spivak, D. V. Suzan, L. A. Sukharev, A. O. Syromyasov, O. B. Feodoritova, I. I. Chuchaev, P. A. Shamanaev, O. S. Yazovtseva, N. G. Yarushkina, “To the seventieth anniversary of Vladimir Fedorovich Tishkin”, Zhurnal SVMO, 21:1 (2019), 111–113
2018
31.
A. S. Andreev, A. V. Ankilov, T. E. Badokina, D. I. Boyarkin, I. V. Boykov, D. K. Egorova, V. Z. Grines, S. A. Grishina, V. K. Gorbunov, Yu. N. Deryugin, E. V. Desyaev, R. V. Zhalnin, I. V. Konopleva, L. R. Kim-Tyan, V. N. Krizsky, S. I. Martynov, T. Ph. Mamedova, S. M. Muryumin, E. E. Peskova, Yu. V. Pokladova, O. V. Pochinka, V. P. Radchenko, I. P. Ryazantseva, S. I. Spivak, L. A. Sukharev, A. O. Syromyasov, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, O. S. Yazovtseva, N. G. Yarushkina, A.-V. Ion, “Velmisov Petr Aleksandrovich (on his seventieth birthday)”, Zhurnal SVMO, 20:3 (2018), 338–340
32.
A. S. Andreev, A. N. Andronov, T. E. Badokina, D. I. Boyarkin, I. V. Boykov, P. A. Vel'misov, V. Z. Grines, S. A. Grishina, V. K. Gorbunov, Yu. N. Deryugin, A. P. Zhabko, R. V. Zhalnin, I. V. Konopleva, L. R. Kim-Tyan, V. N. Krizsky, T. Ph. Mamedova, S. M. Muryumin, O. V. Pochinka, I. P. Ryazantseva, N. V. Savinov, A. R. Sibireva, L. A. Sukharev, V. F. Tishkin, E. V. Foliadova, I. I. Chuchaev, P. A. Shamanaev, N. G. Yarushkina, “In memory of Boris Vladimirovich Loginov”, Zhurnal SVMO, 20:1 (2018), 103–106
2017
33.
E. N. Artem'eva, I. V. Boykov, M. A. Borisov, D. I. Boyarkin, P. A. Vel'misov, V. K. Gorbunov, T. A. Gorshunova, V. Z. Grines, Yu. N. Deryugin, E. V. Desyaev, D. K. Egorova, R. V. Zhalnin, O. E. Kaledin, V. N. Krizsky, E. B. Kuznetsov, B. V. Loginov, T. Ph. Mamedova, S. I. Martynov, N. D. Morozkin, S. M. Muryumin, I. P. Nikitin, O. V. Pochinka, D. V. Pashutkin, A. Yu. Pavlov, E. E. Peskova, I. P. Ryazantseva, V. I. Safonkin, G. A. Smolkin, S. I. Spivak, L. A. Sukharev, A. O. Syromyasov, M. T. Terekhin, V. F. Tishkin, S. A. Firsova, E. A. Chernoivanova, I. I. Chuchaev, P. A. Shamanaev, O. S. Yazovtseva, Z. Ya. Yakupov, “On the 80th anniversary of professor E.V. Voskresensky's birthday”, Zhurnal SVMO, 19:4 (2017), 95–99
34.
P. A. Vel'misov, R. V. Zhalnin, V. T. Zhukov, T. K. Kozubskaya, P. V. Senin, L. I. Sizova, L. A. Sukharev, V. F. Tishkin, B. N. Chetverushkin, I. I. Chuchaev, R. M. Shagaliev, P. A. Shamanaev, V. N. Shchennikov, “Yuri Nikolaevich Deryugin - on his seventieth birthday”, Zhurnal SVMO, 19:2 (2017), 139–141
35.
A. A. Kurkin, S. N. Nagornyh, I. P. Ryazantseva, A. N. Moshkova, T. A. Shemyakina, P. A. Shamanaev, L. A. Sukharev, R. V. Zhalnin, T. Ph. Mamedova, S. M. Muryumin, D. I. Boyarkin, D. K. Egorova, “In memory of Alekseenko Sergey Nikolaevich”, Zhurnal SVMO, 19:1 (2017), 140–142
2016
36.
S. V. Gonchenko, E. V. Zhuzhoma, E. Ya. Gurevich, L. M. Lerman, O. V. Pochinka, V. F. Tishkin, I. I. Chuchaev, L. A. Sukharev, P. A. Shamanaev, R. V. Zhalnin, T. Ph. Mamedova, “Вячеслав Зигмундович Гринес (к семидесятилетию со дня рождения)”, Zhurnal SVMO, 18:4 (2016), 168–171
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