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Inertial manifolds and limit cycles of dynamical systems in Rn
Electronic Journal of Qualitative Theory of Differential Equations. 2019. No. 96. P. 1-11.
Kondratieva L. A., A.V. Romanov
We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in Rn permits reducing the problem of determining asymptotically orbitally stable limit cycles to the Poincaré–Bendixson theory. In the case n = 3 we implement such a scenario for a model of a satellite rotation around a celestial body of small mass and for a biochemical model.
A.V. Romanov, Kondratieva L. A., / Cornell University. Series math "arxiv.org". 2019. No. 1911.03932.
We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in Rn permits reducing the problem of determining asymptotically orbitally stable limit cycles to the Poincare–Bendixson theory. In the
case n = 3 we implement such a scenario for a model of a satellite rotation around a celestial body of small ...
Added: November 13, 2019
A.V. Romanov, Kondratieva L. A., / Cornell University. Series math "arxiv.org". 2019. No. 1911.03932.
We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in Rn permits reducing the problem of determining asymptotically orbitally stable limit cycles to the Poincare–Bendixson theory. In the
case n = 3 we implement such a scenario for a model of a satellite rotation around a celestial body of small ...
Added: November 13, 2019
Kondratieva L. A., / Cornell University Library. Series math.RT "arXiv:1808.06395 [math.RT]". 2019. No. 1911.03932.
We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in Rn permits reducing the problem of determining asymptotically orbitally stable limit cycles to the Poincare–Bendixson theory. In the
case n = 3 we implement such a scenario for a model of a satellite rotation around a celestial body of small ...
Added: November 13, 2019
Моделирование одновременного распространения легальных и контрафактных копий инновационных продуктов
Михайлов А. П., Petrov A., Калиниченко М. И. et al., Математическое моделирование 2013 Т. 25 № 6 С. 54-63
Представлена базовая математическая модель динамики численности легальных и контрафактных пользователей инновационных продуктов на примере компьютерных игр, построенная на основе моделей распространения информации и информационного противоборства. Проведен ее анализ методами теории обыкновенных дифференциальных уравнений, показано качественное соответствие результатов моделирования эмпирическим
данным компании Протекшн Технолоджи (StarForce). ...
Added: October 18, 2014
Romanov A., / Cornell University. Series math "arxiv.org". 2016. No. 1602.08953.
For 3D reaction–diffusion equations, we study the problem of existence or nonexistence of an inertial manifold that is normally hyperbolic or absolutely normally hyperbolic. We present a system of two coupled equations with a cubic nonlinearity which does not admit a normally hyperbolic inertial manifold. An example separating the classes of such equations admitting an ...
Added: June 26, 2016
Mikhailov A. P., A.P.Petrov, Marevtseva N. A. et al., Mathematical Models and Computer Simulations 2014 Vol. 6 No. 5 P. 535-541
This paper is devoted to developing a system of models of information dissemination in society. As a superstructure for the base model, four new mechanisms that have an effect on information disseminating are proposed. For the model with these four echanisms, sufficient conditions of the stability of the nonadherent state are obtained ...
Added: October 12, 2016
S.A.Chistyakova, Dolov M. V., Differential Equations 2012 Vol. 48 No. 8 P. 1180-1182
For a certain class of two-dimensional autonomous systems of differential equations with an invariant curve that contains ovals, we indicate necessary and sufficient conditions for these ovals to be limit cycles of phase trajectories. ...
Added: March 15, 2013
V.S. Samovol, Доклады Академии наук 2012 Vol. 85 No. 1 P. 122-124
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has two purely imaginary eigenvalues, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to pseudonormal form. We prove that the problem of finitely smooth ...
Added: November 27, 2012
Чистякова С. А., Долов М. В., Дифференциальные уравнения 2012 Т. 48 № 8 С. 1193-1195
For a certain class of two-dimensional autonomous systems of differential equations with an invariant curve that contains ovals, we indicate necessary and sufficient conditions for these ovals to be limit cycles of phase trajectories. ...
Added: January 31, 2013
Korolev A. V., СПб. : ЮТАС, 2008
Added: February 8, 2013
Samovol V. S., Математические заметки 2012 Т. 92 № 5 С. 731-746
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of the linearized system has two pure imaginary eigenvalues, all other eigenvalues lying outside the imaginary axis. The reducibility of such systems to pseudonormal form is studied. ...
Added: December 13, 2012
Alexander V. Romanov, / Cornell University. Series math "arxiv.org". 2013. No. 1306.4249.
We construct an example of a one-dimensional parabolic integro-differential equation with nonlocal diffusion which does not have asymptotically finite-dimensional dynamics in the corresponding state space. This example is more natural in the class of evolutionary equations of parabolic type than those known earlier. ...
Added: November 18, 2013
Belkina T. A., Konyukhova N. B., Kurochkin S. V., Журнал вычислительной математики и математической физики 2012 Т. 52 № 10 С. 1812-1846
A singular boundary value problem for a second order linear integrodifferential equation with Volterra and nonVolterra integral operators is formulated and analyzed. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification ...
Added: March 21, 2013
Romanov A., Mathematical notes 2014 Vol. 96 No. 4 P. 548-555
A family of parabolic integro-differential equations with nonlocal diffusion on the circle which have no smooth inertial manifold is presented. ...
Added: September 15, 2014
Romanov A., Dynamics of Partial Differential Equations 2016 Vol. 13 No. 3 P. 263-272
For 3D reaction–diffusion equations, we study the problem of existence or nonexistence of an inertial manifold that is normally hyperbolic or absolutely normally hyperbolic. We present a system of two coupled equations with a cubic nonlinearity which does not admit a normally hyperbolic inertial manifold. An example separating the classes of such equations admitting an ...
Added: June 26, 2016
Romanov A., Математические заметки 2014 Т. 96 № 4 С. 578-587
We construct an example of a one-dimensional parabolic integro-differential equation with nonlocal diffusion which does not have smooth inertial manifold in the corresponding state space. This example is more natural in the class of evolutionary equations of parabolic type than those known earlier. ...
Added: August 19, 2014
Samovol V. S., Доклады Академии наук 2012 Vol. 85 No. 1 P. 122-124
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has two purely imaginary eigenvalues, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to pseudonormal form. We prove that the problem of finitely smooth ...
Added: November 27, 2012
Samovol V. S., Математические заметки 2012 Т. 92 № 6 С. 912-927
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of the linearized system has two pure imaginary eigenvalues, all other eigenvalues lying outside the imaginary axis. The problem of local finitely smooth equivalence of such systems is studied. ...
Added: December 13, 2012
V. Kruglov, O. Pochinka, G. Talanova, Proceedings of the International Geometry Center 2020 Vol. 13 No. 1 P. 49-60
Currently, a complete topological classification has been obtained with respect to the topological equivalence of Morse-Smale flows, [9,7], as well as their generalizations of Ω-stable flows on closed surfaces, [4]. Some results on topological conjugacy classification for such systems are also known. In particular, the coincidence of the classes of topological equivalence and conjugacy of ...
Added: June 28, 2020
Ilya Schurov, Nikita Solodovnikov, / Cornell University. Series math "arxiv.org". 2014. No. 1405.3251.
Slow-fast systems on the two-torus are studied. As it was shown before, canard cycles are generic in such systems, which is in drastic contrast with the planar case. It is known that if the rotation number of the Poincare map is integer and the slow curve is connected, the number of canard limit cycles is ...
Added: May 14, 2014
Bruno A., Parusnikova A., Доклады Академии наук 2011 Т. 438 № 4 С. 439-443
In this work, the methods of power geometry are used to find asymptotic expansions of solutions to the fifth Painlevй equation as x 0 for all values of its four complex parameters. We obtain 30 families of expansions, of which 22 are obtained from published expansions of solutions to the sixth Painlevй equation. Among the ...
Added: April 12, 2012
Kudryashov Y., Goncharuk N. B., Bulletin of the Brazilian Mathematical Society 2017 No. 1
In this article we prove in a new way that a generic polynomial vector field in ℂ² possesses countably many homologically independent limit cycles. The new proof needs no estimates on integrals, provides thinner exceptional set for quadratic vector fields, and provides limit cycles that stay in a bounded domain. ...
Added: April 15, 2016
Logvenkov S. A., Myshkis P. A., Samovol V. S., М. : МЦНМО, 2014
Сборник задач составлен в соответствии с программами курсов по математическому анализу и линейной алгебре для подготовки студентов, обучающихся по специальностям: менеджмент, соцология, государственное и муниципальное управление, психология, прикладная политология. Содержит задачи по следующим разделам: элементы векторной алгебры и аналитической геометрии, матрицы и определители, системы линейных уравнений, дифференциальное и интегральное исчисление функций одной переменной, дифференциальное исчисление ...
Added: February 21, 2015
Александрова И. А., Goncharenko V., Денежкина И. Е. et al., М. : КноРус, 2016
Излагаются основные математические методы, которые применяются при решении экономических и финансовых задач. Основные темы: теория обыкновенных дифференциальных уравнений и численные методы их решения, модели экономи- ческой динамики с непрерывным временем, разностные уравнения и дискретные модели в экономике и финансах, избранные вопросы вариационного исчисления и оптимального управления, уравнения в частных производных первого порядка, уравнения математической физики ...
Added: November 20, 2016