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Slow-fast systems with an equilibrium near the folded slow manifold. / Гельфрейх, Наталия Георгиевна; Иванов, Алексей Валентинович.

в: Regular and Chaotic Dynamics, Том 29, 2024, стр. 376-403.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Гельфрейх, НГ & Иванов, АВ 2024, 'Slow-fast systems with an equilibrium near the folded slow manifold', Regular and Chaotic Dynamics, Том. 29, стр. 376-403. https://doi.org/10.1134/S156035472354002X

APA

Гельфрейх, Н. Г., & Иванов, А. В. (2024). Slow-fast systems with an equilibrium near the folded slow manifold. Regular and Chaotic Dynamics, 29, 376-403. https://doi.org/10.1134/S156035472354002X

Vancouver

Гельфрейх НГ, Иванов АВ. Slow-fast systems with an equilibrium near the folded slow manifold. Regular and Chaotic Dynamics. 2024;29:376-403. https://doi.org/10.1134/S156035472354002X

Author

Гельфрейх, Наталия Георгиевна ; Иванов, Алексей Валентинович. / Slow-fast systems with an equilibrium near the folded slow manifold. в: Regular and Chaotic Dynamics. 2024 ; Том 29. стр. 376-403.

BibTeX

@article{5581a7d6d191431ba687f1b7bdc12e8d,
title = "Slow-fast systems with an equilibrium near the folded slow manifold",
abstract = "We study a slow-fast system with two slow and one fast variables.We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighborhood of the fold. We derive a normal form for the systemin a neighborhood of the pair “equilibrium-fold”and study the dynamics of the normal form. In particular, as the ratio of two time scales tends to zero we obtain an asymptotic formula for the Poincar{\'e} mapand calculate the parameter values for the first period-doubling bifurcation. The theory is applied to a generalization of the FitzHugh – Nagumo system.",
keywords = "period-doubling bifurcation, slow-fast systems",
author = "Гельфрейх, {Наталия Георгиевна} and Иванов, {Алексей Валентинович}",
year = "2024",
doi = "10.1134/S156035472354002X",
language = "English",
volume = "29",
pages = "376--403",
journal = "Regular and Chaotic Dynamics",
issn = "1560-3547",
publisher = "МАИК {"}Наука/Интерпериодика{"}",

}

RIS

TY - JOUR

T1 - Slow-fast systems with an equilibrium near the folded slow manifold

AU - Гельфрейх, Наталия Георгиевна

AU - Иванов, Алексей Валентинович

PY - 2024

Y1 - 2024

N2 - We study a slow-fast system with two slow and one fast variables.We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighborhood of the fold. We derive a normal form for the systemin a neighborhood of the pair “equilibrium-fold”and study the dynamics of the normal form. In particular, as the ratio of two time scales tends to zero we obtain an asymptotic formula for the Poincaré mapand calculate the parameter values for the first period-doubling bifurcation. The theory is applied to a generalization of the FitzHugh – Nagumo system.

AB - We study a slow-fast system with two slow and one fast variables.We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighborhood of the fold. We derive a normal form for the systemin a neighborhood of the pair “equilibrium-fold”and study the dynamics of the normal form. In particular, as the ratio of two time scales tends to zero we obtain an asymptotic formula for the Poincaré mapand calculate the parameter values for the first period-doubling bifurcation. The theory is applied to a generalization of the FitzHugh – Nagumo system.

KW - period-doubling bifurcation

KW - slow-fast systems

UR - https://www.mendeley.com/catalogue/a9e541d0-a694-3711-98e8-c9f48329bf00/

U2 - 10.1134/S156035472354002X

DO - 10.1134/S156035472354002X

M3 - Article

VL - 29

SP - 376

EP - 403

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

SN - 1560-3547

ER -

ID: 127635837