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Ukrainian Mathematical Journal

, Volume 60, Issue 1, pp 66–77 | Cite as

On one bifurcation in relaxation systems

  • A. Yu. Kolesov
  • E. F. Mishchenko
  • N. Kh. Rozov
Article

Abstract

We establish conditions under which, in three-dimensional relaxation systems of the form {fx066-01}, where 0 < ε << 1, |μ| << 1, and ƒ, gC , the so-called “blue-sky catastrophe” is observed, i.e., there appears a stable relaxation cycle whose period and length tend to infinity as μ tends to a certain critical value μ*(ε), μ*(0) 0 = 0.

Keywords

Unstable Manifold Stable Manifold Relaxation Oscillation Node Domain Relaxation System 
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

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • A. Yu. Kolesov
    • 1
  • E. F. Mishchenko
    • 2
  • N. Kh. Rozov
    • 3
  1. 1.Yaroslavl UniversityYaroslavlRussia
  2. 2.Mathematical InstituteRussian Academy of SciencesMoscowRussia
  3. 3.Moscow UniversityMoscowRussia

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