Relaxation oscillations, parasitics, and singular perturbations

The rate at which solutions of
\lambda \dot{x} = F(x, y), \dot{y} = G(x, y), 0 \leq \lambda \ll 1, x
an
n
-vector,
y
an
m
-vector, approach the solutions of
F(x, y) = 0, \dot{y} = G(x, y)
is obtained. Physically, this is important in the study of parasitics, in relaxation oscillations, and in other applications. The behavior of solutions of the Liénard equation near a jump is also deduced. This result is pertinent for certain relaxation oscillations.