= Weak-damping heteroclinic splitting of a tilted quartic oscillator
{title2=$\kappa=\lambda/5\pm\sqrt2\,\varepsilon+\cdots$}
For the <imperfect soft Duffing-van der Pol oscillator> at positive small $\lambda$ and $|\varepsilon|\ll\sqrt\lambda$, the symmetric connection of the <Hamiltonian system> is $v=\sqrt\lambda\tanh(\sqrt{\lambda/2}\,t)$. Its damping integral is $4\lambda^{3/2}(\kappa-\lambda/5)/(3\sqrt2)$. The two <saddle equilibrium> barrier heights differ by $-4\varepsilon\lambda^{3/2}/3$ to first order. Equating the <energy> change to this difference gives the two oppositely directed connection curves in the display. These are weak-damping asymptotic curves, not exact global formulas at order-one parameters.
// Destination: astrophysical-fluid-dynamics.bigb
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