 Solution

The term $ru$ is unrestricted growth of species $u$, and $-r{u}^2$ represents its density-dependent self-limitation, with scaled carrying capacity one. The interaction $-ruv$ suppresses $u$ in the presence of species $v$.

Species $v$ has intrinsic growth $v$ and suppression $-\beta uv$ by $u$. Thus both interspecific effects are harmful: this is a competition model, with no self-limitation term for $v$. Its unbounded growth when $u$ disappears is a consequence of that modeling choice. The parameter $r$ is the growth-time ratio, while $\beta$ measures the effect of $u$ on $v$.