A model of two populations competing for resources takes the form

$$\begin{aligned} \frac{d n_{1}}{d t} &=r_{1} n_{1}\left(1-n_{1}-a_{12} n_{2}\right) \\ \frac{d n_{2}}{d t} &=r_{2} n_{2}\left(1-n_{2}-a_{21} n_{1}\right) \end{aligned}$$

where all parameters are positive. Give a brief biological interpretation of $a_{12}, a_{21}, r_{1}$ and $r_{2}$. Briefly describe the dynamics of each population in the absence of the other.

Give conditions for there to exist a steady-state solution with both populations present (that is, $n_{1}>0$ and $n_{2}>0$ ), and give conditions for this solution to be stable.

In the case where there exists a solution with both populations present but the solution is not stable, what is the likely long-term outcome for the biological system? Explain your answer with the aid of a phase diagram in the $\left(n_{1}, n_{2}\right)$ plane.