How does this man get his currents?

[Slightly]

How does this man get his currents?

1. Homework Statement [/b]

I'm having a time trying to figure out how these currents are made.

I don't understand his notation. It seems simple, but it is going the opposite way of what it should be doing because of the diode, right?

Attached is the circuit and his formulations of the currents.

 

[mfb]

f(...) is the current through the diode as function of its voltage. As long as f is unknown, the third equation says nothing interesting.

 

[Slightly]

We are trying to find what f is.

Turns out that this turns into the van de pol equation.