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


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].


Phase Portrait Unstable Manifold Degenerate System Relaxation System Node Cycle 
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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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