thevenin question

Can we apply Thevenin's equivalent circuit to a network with non-zero initial conditions?

I don't see why not. I don't think initial conditions is a restriction on using thevenin. Check a basic circuit analysis text or the web for an exact answer.

Non-zero conditions? Thevenin is a theoretical reduction of a circuit's component parts to their RESISTIVE equivalent. A 10k resistor is a 10k resistor is a 10k resistor. It is still the same at 10 volts or at 100 volts, 10 amps or at 100 amps. The purpose of Thevenizing a circuit is to "look" at it from a power supply's perspective. It lets an engineer ask the question; "What is this load?". The term "non-zero" is not quite correct. What you need to do is take the "instantaneous value" of the circuit. Remember physics class? So, calculate (Thevenize) your circuit, tweak the pots, Thevenize again, tweak again, Thevenize, tweak, Theve....

Plot the results. Take a pill. See a doctor.

um... how about with the Laplace transform of the circuit?

yes, laplace is probably what you're looking for, in fact that's sorta what it's all about. your initial conditions go in as voltage or current sources in the laplace transformed circuit, and then you can use normal node/mesh analysis to examine the circuit in the S-domain, then use laplace transform to go back to the time domain as needed. someone can correct me if i'm wrong, it's been a while since I had a circuits course.