= Solution
The <linearization> of this reduction of the <FitzHugh-Nagumo model> at its trivial <equilibrium point> is
$$
L=\begin{pmatrix}0&1&0\\-1&-2&1\\-c/2&0&d/2\end{pmatrix},\qquad
\det(mI-L)=m^3+(2-d/2)m^2+(1-d)m+(c-d)/2.
$$
A double zero <eigenvalue> requires both the constant and linear coefficients to vanish. Hence \b[the codimension-two point is]
$$
\boxed{(c_*,d_*)=(1,1).}
$$
There the polynomial is $m^2(m+3/2)$. The <kernel of a linear map> of $L$ is one-dimensional, so its zero <eigenvalue> has a nontrivial size-two block in <Jordan normal form>. This is a reflection-symmetric double-zero point of <Bogdanov–Takens bifurcation> type, with one stable direction; the nonlinear coefficients are computed below rather than assumed.
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