How does stability analysis of Lotka-Volterra system differ from stability analysis on a normalized version?
Normalized LV system is such where the coefficients have been "aggregated" so that the system has less variable parameters. I find it confusing to infer how it alters critical points though, since:
Since it's essentially describing the same system, then it should have same critical points.
However the new parametrization may give different critical points than the original parametrization due to them having been shifted by the aggregating of coefficients.
I saw text that did stability analysis on normalized system and made it seem as if it's "as informative" as studying the original system. And I didn't understand why:
https://www.maths.dur.ac.uk/%7Ektch24/term1Notes(10).pdf, p. 2
The rescaled equation does not give new critical points. Notice that $$\hat x = 1 = \frac d c x \implies x = \frac c d,$$ $$\hat y = 1 = \frac b a y \implies y = \frac a b$$ and $(x,y) = (\frac c d , \frac a b)$ is a steady state of the non-normalize equations.
The normalized system gives the same information because essentially, the parameters $a,b,c,d$ are "summarized" in $\gamma$ (I am using the notations from your reference) and $\hat x, \hat y$ are a percentage, essentially.