We have the following system (prey-predator): \begin{cases} h'=rh-\frac{\alpha h}{1+\beta h}p & \\ p'=-ap+\frac{\gamma h}{1+\beta h}p & \end{cases} I have to rewrite it so that it looks as simple as possible. I did the following:
$h=\bar{h}H$;
$p=\bar{p}P$;
$t=\bar{t}\tau.$
After that I got the system:
\begin{cases} H'=H-\frac{HP}{1+H} & \\ P'=-\frac{a}{r}P+\frac{\frac{\gamma}{r\beta}}{1+H}HP & \end{cases} I got these because I did the notations: $\bar{t}=\frac{1}{r},\bar{p}=\frac{r}{\alpha} $ and $\bar{h}=\frac{1}{\beta}.$
Is it correct what I did? or did I not choose the right notations?