Solution
= Solution
At $r=1$, the Jacobian at the origin is
$$
J=\begin{pmatrix}
-1&1&0\\
1&-1&0\\
0&0&-1
\end{pmatrix}.
$$
Its <eigenvalues> are $0,-2,-1$. The zero <eigenvalue> makes the equilibrium nonhyperbolic.
= Solution
At $r=1$, the Jacobian at the origin is
$$
J=\begin{pmatrix}
-1&1&0\\
1&-1&0\\
0&0&-1
\end{pmatrix}.
$$
Its <eigenvalues> are $0,-2,-1$. The zero <eigenvalue> makes the equilibrium nonhyperbolic.