I have following set of equations,
$\frac{dy(t)}{dt}=k z(t) - 3 k y(t) - y(t)^2 + \epsilon_1 (M-z(t))^2$
$\epsilon_2 \frac{dz(t)}{dt}=Mz(t) - z(t) y(t) - 2 \epsilon_2 y(t) + 2 \epsilon_1 \epsilon_2 (M-z(t))^2$
From above, I can't even solve the unperturbed problem if the perturbation is around only one of the $\epsilon_1$ or $\epsilon_2$.
Now my question is: Is it possible to do perturbation theory for two small parameters and not just one?
One more thing to note is: the equations are singular for $\epsilon_2$ but regular for $\epsilon_1$.
Any suggestion, reference or help on how to go about solving these equations will be of great help.