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Differential Equations

, Volume 44, Issue 2, pp 161–175 | Cite as

Blue sky catastrophe in relaxation systems with one fast and two slow variables

  • S. D. Glyzin
  • A. Yu. Kolesov
  • N. Kh. Rozov
Ordinary Differential Equations

Abstract

We establish conditions under which three-dimensional relaxational systems of the form
$$ \dot x = f(x,y,\mu ),\varepsilon \dot y = g(x,y),x = (x_1 ,x_2 ) \in \mathbb{R}^2 ,y \in \mathbb{R}, $$
where 0 ≤ ε ≪ 1, |µ| ≪ 1, and f, gC , exhibit the so-called blue sky catastrophe [the appearance of a stable relaxational cycle whose period and length tend to infinity as µ tends to some critical value µ*(ε), µ*(0) = 0].

Keywords

Phase Portrait Unstable Manifold Degenerate System Relaxation System Node Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  • S. D. Glyzin
    • 1
    • 2
  • A. Yu. Kolesov
    • 1
    • 2
  • N. Kh. Rozov
    • 1
    • 2
  1. 1.Yaroslavl State UniversityYaroslavlRussia
  2. 2.Moscow State UniversityMoscowRussia

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