Cubic amplitude saturation
= Cubic amplitude saturation
{title2=$R'=aR-R^3$}
For $a>0$, the positive amplitude <ordinary differential equation> $R'=aR-R^3$ has solution $R(t)=\sqrt a[1+(a/R_0^2-1)e^{-2at}]^{-1/2}$. This follows from the <logistic differential equation> for $R^2$. Every $R_0>0$ approaches $\sqrt a$ as a <monotone function>, and the positive distance to this limit decreases; an oscillating complex wave carrying this amplitude has no ordinary monotone ordering.