Q: How to prove that there is no periodic orbit in this autonomous system?(ODE) Consider the autonomous system below with the parameters $a\neq 0$ and $mn \neq 0$:
$$\begin{cases}
\displaystyle\frac{dx}{dt} &=-y+mxy+ny^2\\ 
\displaystyle\frac{dy}{dt} &=x+ax^2
\end{cases}$$
How to prove that there is no periodic orbit in this autonomous system?
I think maybe Dulac's criterion is the tips of this question, but I haven't found the Dulac's Function yet.
