multiple time scale dynamics with two fast variables and one slow ...

in the FitzHugh-Nagumo equation explains why n-homoclinic and n-periodic
orbits are expected to be found at parameter values very close to a primary 1-
homoclinic orbit. Section 5.6 presents two further observations. We identify
where a canard explosion [86] occurs and we note the existence of two different
types of mixed-mode oscillations in the system.
5.3 Fast-Slow Decomposition of Homoclinic Orbits
We introduce notation used in our earlier work [56]. The critical manifold of
(5.1) is given by:
C0={(x1, x2, y)∈R 3 : x2= 0 and y= f (x1)+ p}
It is normally hyperbolic away from the two fold points x1,± with x1,− < x1,+
which are found by solving f ′ (x1)=0 as the local minimum and maximum of
the cubic f . Hence C0 splits into three parts:
Cl={x1