= Quadratic Bogdanov–Takens unfolding
{title2=$\dot x=y,\quad\dot y=-\lambda+\mu y+x^2+xy$}
For $\lambda>0$, the <equilibrium points> are $x=\pm\sqrt\lambda$, $y=0$. The positive branch is a saddle; the negative branch has a subcritical <Hopf bifurcation> at $\mu=\sqrt\lambda$. A <homoclinic orbit> occurs at $\mu=(5/7)\sqrt\lambda+O(\lambda)$ near the double-zero point. Between this homoclinic curve and the Hopf curve, an unstable <periodic orbit> surrounds a stable <equilibrium point>. The factor $5/7$ follows from a <Melnikov energy-balance method>, using the integrals of $v^2$ and $uv^2$ along the leading conservative saddle loop.
// Destination: dynamical-systems.bigb
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