Consider the 2-dimensional flow

$$\dot{x}=-\mu x+y, \quad \dot{y}=\frac{x^{2}}{1+x^{2}}-\nu y$$

where $x(t)$ and $y(t)$ are non-negative, the parameters $\mu$ and $\nu$ are strictly positive and $\mu \neq \nu$. Sketch the nullclines in the $x, y$ plane. Deduce that for $\mu<\mu_{c}$ (where $\mu_{c}$ is to be determined) there are three fixed points. Find them and determine their type.

Sketch the phase portrait for $\mu<\mu_{c}$ and identify, qualitatively on your sketch, the stable and unstable manifolds of the saddle point. What is the final outcome of this system?