On one bifurcation in relaxation systems

We establish conditions under which, in three-dimensional relaxation systems of the form {fx066-01}, where 0 < ε << 1, |μ| << 1, and 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. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 63–72, January, 2008.