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Differential Equations with a Small Parameter and Multipeak Oscillations Научная публикация

Журнал

Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797

Вых. Данные

Год: 2024, Том: 18, Номер: 1, Страницы: 18-35 Страниц : 18 DOI: 10.1134/s1990478924010034

Ключевые слова

ordinary differential equation, small parameter, limit cycle, invariant manifold, Poincar´e map, kinetic model, multipeak self-oscillations

Авторы

Chumakov G.A. ^1,3 , Chumakova N.A. ^2,3

Организации

1	Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2	Boreskov Institute of Catalysis, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
3	Novosibirsk State University, Novosibirsk, 630090, Russia

Информация о финансировании (2)

1	Институт математики им. С.Л. Соболева СО РАН	FWNF-2022-0005
2	Институт катализа им. Г.К. Борескова СО РАН	FWUR-2024-0037

In this paper, we study a nonlinear dynamical system of autonomous ordinary differential equations with a small parameter µ such that two variables x and y are fast and another one z is slow. If we take the limit as µ → 0, then this becomes a “degenerate system” included in the one-parameter family of two-dimensional subsystems of fast motions with the parameter z in some interval. It is assumed that in each subsystem there exists a structurally stable limit cycle lz. In addition, in the complete dynamical system there is some structurally stable periodic orbit L that tends to a limit cycle lz0 for some z = z0 as µ tends to zero. We can define the first return map, or the Poincar´ e map, on a local cross section in the hyperplane (y,z) orthogonal to L at some point. We prove that the Poincar´ e map has an invariant manifold for the fixed point corresponding to the periodic orbit L on a guaranteed interval over the variable y, and the interval length is separated from zero as µ tends to zero. The proved theorem allows one to formulate some sufficient conditions for the existence and/or absence of multipeak oscillations in the complete dynamical system. As an example of application of the obtained results, we consider some kinetic model of the catalytic reaction of hydrogen oxidation on nickel.

Chumakov G.A. , Chumakova N.A.
Differential Equations with a Small Parameter and Multipeak Oscillations
Journal of Applied and Industrial Mathematics. 2024. V.18. N1. P.18-35. DOI: 10.1134/s1990478924010034 Scopus РИНЦ OpenAlex

Чумаков Г.А. , Чумакова Н.А.
Дифференциальные уравнения с малым параметром и многопиковые автоколебания
Сибирский журнал индустриальной математики. 2024. Т.27. №1. 8 :1-18. DOI: 10.33048/SIBJIM.2024.27.107 РИНЦ

Поступила в редакцию:	25 сент. 2023 г.
Принята к публикации:	7 февр. 2024 г.
Опубликована в печати:	26 апр. 2024 г.
Опубликована online:	26 апр. 2024 г.

Scopus:	2-s2.0-85191370942
РИНЦ:	66926146
OpenAlex:	W4395679105

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