Krill is the main food source for baleen whales. The following model has been proposed for the coupled evolution of populations of krill and whales, with $x(t)$ being the number of krill and $y(t)$ being the number of whales:

$$\begin{array}{r} \frac{d x}{d t}=r x\left(1-\frac{x}{K}\right)-a x y \\ \frac{d y}{d t}=s y\left(1-\frac{y}{b x}\right) \end{array}$$

where $r, s, a, b$ and $K$ are positive constants.

Give a biological interpretation for the form of the two differential equations.

Show that a steady state is possible with $x>0$ and $y>0$ and write down expressions for the steady-state values of $x$ and $y$.

Determine whether this steady state is stable.