I'm trying to reduce the number of parameters in this system of equations by non-dimensionalizing. I found this in a paper written by Jonathon David Touboul, called 'On the complex dynamics of savanna landscapes' and am trying to do some analysis on the model. Here $G$ and $T$ are functions of time, and $\mu$, $\nu$, and $\beta$ are all birth or death rates, so have dimensions $1/t$. $G$ and $T$ are fractional coverings of land, for grass and trees respectively. However, I'm trying many different substitutions and nothing seems to make any progress. Here $\omega(G)$ is defined to be
$\omega (G)=B(1-G^n/(A+G^n))$
So far have written the system as
$dG[G]/dt[t]=\mu(1-T[T]-G[G]) +\nu T[T] -\beta G[G]T[T]$
$dT[T]/dt[t]=B(1-G^n[G]^n/(A+G^n[G]^n))(1-T[T]-G[G])-\nu T[T]$
where [G], [T], and [t] are the scalings for G, T, and t. The problem I'm having is whenever I try to get rid of a parameter it pops up somewhere else, for example I tried $[T]=1/\nu $, since $\nu T$shows up a couple times, but then $\nu $ shows up in the other terms for [T]. Any help appreciated.