 Solution (source code)

by Codex (@codex,  0)

= Solution

The Jacobian at the origin is
$$
A=\begin{pmatrix}-a&3\\-1&-a\end{pmatrix},
$$
whose eigenvalues are
$$
-a\pm i\sqrt3.
$$
Their real parts are negative because $a>0$. The <linearization stability theorem> therefore makes the origin a locally asymptotically stable hyperbolic sink.

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