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## Inertial Manifolds and Limit Cycles of Dynamical Systems in Rn

Cornell University Library
,
2019.
No. 1911.03932.

Kondratieva L. A.

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 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., A.V. Romanov, Electronic Journal of Qualitative Theory of Differential Equations 2019 No. 96 P. 1-11

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 ...

Added: December 22, 2019

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

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

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

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

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

A.V. Romanov, / Cornell University. Series arXiv "math". 2022. No. 2210.00499.

We present a class of one-dimensional systems of nonlinear parabolic equations for which long-time phase dynamics can be described by an ODE with a Lipschitz vector field in R^n. In the considered case of the Dirichlet boundary value problem sufficient conditions for a finite-dimensional reduction turn out to be much wider than the known conditions ...

Added: October 5, 2022

Aleksandr V. Romanov, AIMS MATHEMATICS 2021 Vol. 6 No. 12 P. 13407-13422

We consider the class of dissipative reaction-diffusion-convection systems on the circle and obtain conditions under which the final (at large times) phase dynamics of a system can be described by an ODE with Lipschitz vector field in RN. Precisely in this class, the first example of a parabolic problem of mathematical physics without the indicated ...

Added: September 18, 2021

Kolobianina A., Kruglov V., Журнал Средневолжского математического общества 2020 Т. 22 № 4 С. 434-441

In this paper, we consider the class of Ω-stable flows on surfaces, i.e. flows on surfaces with the non-wandering set consisting of a finite number of hyperbolic fixed points and a finite number of hyperbolic limit cycles. The class of Ω-stable flows is a generalization of the class of Morse-Smale flows, admitting the presence of ...

Added: November 27, 2020

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

A.V. Romanov, Mathematical Notes 2023 Vol. 113 No. 2 P. 267-273

We consider a class of one-dimensional systems of nonlinear parabolic equations whose phase dynamics at large time can be described by ODE with a Lipschitz vector field in R^n. In the case of the Dirichlet boundary-value problem considered here, sufficient conditions for the finite-dimensional reduction turn out to be essentially wider than the known similar ...

Added: November 27, 2022

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

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

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

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020

Borzykh D., ЛЕНАНД, 2021

Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...

Added: February 20, 2021

В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80

Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...

Added: May 3, 2017

Красноярск : ИВМ СО РАН, 2013

Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...

Added: November 18, 2013

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148

In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...

Added: May 17, 2017

Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600

We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...

Added: October 25, 2018

Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188

The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...

Added: December 2, 2019