Blue sky catastrophe in relaxation systems with one fast and two slow variables
type: Item
instance of: scholarly article
title: Blue sky catastrophe in relaxation systems with one fast and two slow variables
zbMATH Open document ID: 1211.37065
DOI: 10.1134/S0012266108020031
author: S. D. Glyzin
author: A. Yu. Kolesov
author: N. Kh. Rozov
published in: Differential Equations
publication date: 2010-01-15T00:00:00Z
review text: The authors consider the three-dimensional relaxation system \(\dot{x}=f(x,y,\mu )\), \(\varepsilon \dot{y}=g(x,y)\), \(x=(x_1,x_2)\in\mathbb R^2\), \(y\in\mathbb R\). Here \(0<\varepsilon \ll 1\), \(|\mu |\ll 1\), \(f,g\in C^\infty\). Under a number of standard conditions described in [\textit{E. F. Mishchenko} and \textit{N. Kh. Rozov}, Differential equations with a small parameter and relaxation oscillations. Moskva: Nauka (1975; Zbl 0850.34001)], a blue sky catastrophe can take place in the described system providing the existence of classical relaxation oscillations.
Mathematics Subject Classification ID: 37G35
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 5659337
zbMATH Keywords: blue sky catastrophe
zbMATH Keywords: relaxation system
zbMATH Keywords: saddle-node
zbMATH Keywords: non-local bifurcation
Wikidata QID: Q59448556
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
cites work: Q3371991
cites work: Q4884302
cites work: Q4264342
cites work: Q4864744
full work available at URL: s0012266108020031
OpenAlex ID: W2080644162
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description: scientific article; zbMATH DE number 5659337