I have equations such as
$\frac{dx}{dt} = y \\ \frac{dy}{dt} = \mu y + x - x^{2} + xy$
This system is known to be homoclinic bifurcation at the origin. To find the critical value of $\mu_{c}$, one found $\mu_{c}$ by the numerical calculation. In this case, how can I find critical value of $\mu_{c}$ where the bifurcation occurs?