Asymptotics of Solutions of Autonomous Singularly Perturbed Equations when the Stability of the Equilibrium Position Changes at Several Points

Abstract

Considers a system consisting of 2n equations with fast variables and one equation with a slow variable. The first approximation matrix of the system of fast variables has 2n pairwise complex conjugate eigenvalues. The stability of the equilibrium position, a system of fast variables, is influenced by all eigenvalues. Early studies considered cases where the stability of the equilibrium position is affected by only one pair of complex conjugate eigenvalues. The problem of delaying the solution of a system of fast variables near an unstable equilibrium position has been solved. The delay time for the decision is determined.