I have some questions concerning fast slow system like the van der pol equation
say we have $\epsilon x′_1=-\frac13 x_1^3+x_1 − x_2$ and $x′_2= x_1$
Does $\epsilon x'_1$ means that $x_1$ is faster than $x_2$?
Why do we put $\epsilon = 0$?
When this happens, the graph we get means what?
I appreciate every help and thank you for your time
1) yes, because if you divide by $\epsilon$, the derivative of $x_1$ would be very large for small $\epsilon$. (note that usually one writes the equations with different signs)
2) I think nobody does it otherwise it would be stupid to write a number that is always zero. Instead one considers small $\epsilon$ (to make the difference in speed more prominent, because math like extremes)
3) graph of what?