$54\mathrm{.}3.$ Consider the three$-$species ecosystem

$\frac{dF}{dt}=F(-a+bR-k_{1}G)$

$\frac{dR}{dt}=R(c-dF-k_{2}G)$

$\frac{dG}{dt}=G(k+k_{3}F-k_{4}R)$

assuming all coefficients are positive constants.

$(a)IfG=0,$ show that this represents a predator$-$prey situation. $(Which$

species $is$ the predator, and which $is$ the prey?$)$

$(b)IfG0,$ explain $in$ ecological terms, the interactions $of$ species $G$

with species $R$ and FNOT solve any differential equations.