TY - JOUR AU - A. Yu. Kolesov AU - E. F. Mishchenko AU - N. Kh. Rozov PY - 2008/01/25 Y2 - 2024/03/28 TI - On one bifurcation in relaxation systems JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 60 IS - 1 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3137 AB - 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