= Primary parametric resonance of a two-to-one oscillator pair
{title2=$\lambda^2=(b^2-\alpha^2)/4$}
For weak quadratic coupling between <frequencies> one and two, the first oscillator's <complex amplitude> can obey $2iA_T+\alpha A+b\overline A=0$ with a constant real second-oscillator amplitude $b$. In real coordinates this is a linear slow system with squared growth rate $(b^2-\alpha^2)/4$. Exponential amplification occurs when the modulation amplitude exceeds detuning, $|b|>|\alpha|$. The <method of multiple scales> is valid over bounded slow time while the physical amplitudes remain in the weak-coupling regime. At equality the slow matrix can have a <Jordan block> and produce linear growth for some initial phases.
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