Given the Lotka-Volterra system: $$\frac{dR}{dt}=aR-bRF$$ $$\frac{dF}{dt}=-cF+dRF$$
I think Buckingham-$\pi$ predicts that - since there are 7 variables (R, F, a, b, c, d, t), and 2 units (# of animals, time), the system can be expressed in 7 - 2 = 5 dimensionless variables.
However when I do the standard nondimensionalization, I get: $$\frac{dx}{d\tau}=x(1-y)$$ $$\frac{dy}{d\tau}=\mu y(x-1)$$
Where $\tau$ stands for dimensionless time. There are only 4 variables total, not five. What went wrong? I've been using Buckingham-Pi for other systems in the same way and they've worked out fine.