In this paper an alternative approach to the method of asymptotic expansions for the study of a
singularly perturbed linear system with multiparameters and multiple time scales is developed. The
method consists of developing a linear non-singular transformation that transforms an arbitrary
n—time scale system into a diagonal form. Furthermore, a dichotomy transformation is employed to
decompose the faster subsystems into stable and unstable modes. Fast, slow, stable and unstable
modes decomposition processes provide a modern technique to find an approximate solution of the
original system in terms of the solution of an auxiliary system. This method yields a constructive and
computationally attractive way to investigate the system.
