On one bifurcation in relaxation systems

  • A. Yu. Kolesov Ярослав. ун-т, Россия
  • E. F. Mishchenko
  • N. Kh. Rozov Моск. ун-т, Россия


We establish conditions under which, in three-dimensional relaxation systems of the form $$\dot{x} = f(x, y, \mu),\quad, \varepsilon\dot{y} = g(x, y),\quad x= (x_1, x_2) \in {\mathbb R}^2,\quad y\in{\mathbb R },$$ where $0 < ε << 1, |μ| << 1, ƒ, g ∈ C_{∞}$ 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.
How to Cite
Kolesov, A. Y., E. F. Mishchenko, and N. K. Rozov. “On One Bifurcation in Relaxation Systems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 1, Jan. 2008, pp. 63–72, https://umj.imath.kiev.ua/index.php/umj/article/view/3137.
Research articles