2017
Том 69
№ 9

All Issues

On one bifurcation in relaxation systems

Kolesov A. Yu., Mishchenko E. F., Rozov N. Kh.

Full text (.pdf)


Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 1, pp 66-77.

Citation Example: Kolesov A. Yu., Mishchenko E. F., Rozov N. Kh. On one bifurcation in relaxation systems // Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 63–72.

Full text