I have a 2D system of ODEs where $(x,y) \in [0,1]\times(0,1]$ as follows: $$ \dot{x} = a\frac{x(1-x)}{y} - bxy $$ $$ \dot{y} = cx(1-y) - dy$$ where $a,b,c,d \in \mathbb{R}$. The system is clearly is undefined at $y=0$. Furthermore, $$ \lim_{(x,y) \rightarrow (0,0)}{\frac{x(1-x)}{y}}$$ is undefined.
However, the dynamics still behave as if there is an unstable node at $(0,0)$. Is it fair to call $(0,0)$ a source? Is there a more rigorous way of addressing this scenario? Or are we not to consider (0,0) at all? While it is not defined, the point still seems very useful in describing the dynamics.