For the mathematical simulation of many processes of the real world, systems of nonlinear differential equations are used which contain a small positive parameter µ participting in the determination of the time scale of the process. In general, the equations have the form


dt = Y (t, y, µ), y(t0) = y0, (1.1.1)

where y(t) ∈ Rn is the vector of the state of a system at a point of time t ∈ R, R = (−∞,+∞), t0 ∈ R+, Y : R × Rn ×M → Rn, M = (0, 1], µ is a small parameter.