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


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.


Unstable Manifold Stable Manifold Relaxation Oscillation Node Domain Relaxation System 
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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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