= Positive-quadrant Dulac multiplier for quadratic activation
{title2=$\nabla\cdot(u^{-2}(f,g))=(b-1)/u^2$}
For the diffusionless <quadratic activator-inhibitor model>, choose the <Dulac function> $u^{-2}$. Then $u^{-2}f=1/v-b/u$ and $u^{-2}g=1-v/u^2$, giving divergence $(b-1)/u^2$. For $0<b<1$ it is strictly negative throughout the simply connected positive quadrant. <Green's theorem> rules out a periodic orbit: its boundary flux would be zero because the rescaled vector field is tangent to the orbit, while its interior divergence integral would be negative.
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