How do I quantitatively describe a system with 2 parallel diodes and a current source
Have a search/read of the Wiki and other resources on "diode modelling". The AllAboutCircuits page is useful, and this excellent paper from Berkeley, plus this paper on the SPICE diode model.

Here is a sample Maxima session using the ideal Shockley equation (not very accurate, but can be built on) to calculate the circuit for two slightly different diodes. Hope it's of some use to get you started. Note that as Olin says, (and I assumed) this is purely Academic, and unless you really go to town with the math, unlikely to be of much use in real life.