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I have the following system of equations:

$\dot{x}= x + y^2 + yz $
$\dot{y}= -y + z^2 +xz $
$\dot{z}= -2z +x^2 +xy $

I have to provide 2nd order Taylor expansion of 1. the local stable manifold $W_{loc}^s(0)$ , the local unstable manifold $W^u_{loc}(0)$ and the strong stable manifold around $(0,0,0)$. I know that these manifolds are invariant. Any help?

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