Define new variables $$\backslash$tau$=$k$\_1$e$\_$ot$,$S$=$s$/$K$\_$s$,$C$=$c$/$e$\_0$$ where $K$\_$s$=($k$\_\{-1\}+$k$\_2)/$k$\_1$$ and rescale the two equations. Show that they can be written

$$$\backslash$cfrac$\{$dS$\}\{$d$\backslash$tau$\}=-$S$+(1-\backslash$eta$+$S$)$C$$

$$$\backslash$varepsilon$\backslash$cfrac$\{$dC$\}\{$d$\backslash$tau$\}=$S$-(1+$S$)$C$$

with the dimensionless parameters $$\backslash$varepsilon$=$e$\_$o$/$K$\_$s$ and $$\backslash$eta$=$k$\_2/($k$\_\{-1\}+$k$\_2)$$$.$