On one bifurcation in relaxation systems

• Date: 2008
• Main Authors: Kolesov, A. Yu., Mishchenko, E. F., Rozov, N. Kh., Колесов, А. Ю., Мищенко, Е. Ф., Розов, Н. Х.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3137
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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