Solution
= Solution
The Jacobian is
$$
J(x,y)=\begin{pmatrix}0&1\\8x/(x^2+1)&-3\end{pmatrix}.
$$
At $(1,0)$ its <eigenvalues> are $1,-4$, so this point is a saddle. At $(-1,0)$ they are $(-3\pm i\sqrt7)/2$, so this point is a stable spiral.
= Solution
The Jacobian is
$$
J(x,y)=\begin{pmatrix}0&1\\8x/(x^2+1)&-3\end{pmatrix}.
$$
At $(1,0)$ its <eigenvalues> are $1,-4$, so this point is a saddle. At $(-1,0)$ they are $(-3\pm i\sqrt7)/2$, so this point is a stable spiral.