The Phenomenon of Delaying Loss of Stability in the Theory of Singular Perturbations

Abstract

This paper considers an autonomous system of singularly perturbed equations of fast variables, consisting of four first-order equations and one equation of a slow variable. The first approximation matrix has pairwise complex conjugate eigenfunctions. The system has an equilibrium position, and the stability of the equilibrium position is lost at a certain value of the slow variable. At this point, the real parts of all eigenfunctions vanish. Early works considered cases when the stability of the equilibrium position is lost by one pair of complex conjugate eigenfunctions. The problem of the phenomenon of prolongation of the loss of stability of the equilibrium position has been solved.