Nondimensionalizing Analysis

Nondimensionalization gives an equation the viewport of being analytically defineable as big or small relative to 1.

Making Terms independent of control parameters by nondimensionalization for easy graphical analysis

In example 3.7 of Nonlinear Dynamics and Chaos the substituted equation $\dot{N}=\underset{\text{gain term}}{\underbrace{RN\left(1-\frac{N}{K}\right)}}-\underset{\text{loss term}}{\underbrace{\frac{B{N}^2}{A^2+B^2}}}$ nondimensionalising substitutions are found ($\frac{dx}{d\tau }=rx\left(1-\frac{x}{k}\right)-\underbrace{\frac{x^2}{1+x^2}}\_\text{loss term}$) such that the loss term doesn’t depend on any of the final control parameters $r,k$. This way we can equate $rx\left(1-\frac{x}{k}\right)=\frac{x^2}{1+x^2}$ and in graphical analysis the loss-term function won’t move (because independent on parameters $r,k$), which makes intersections fixed points much easier to spot.