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Is there a way to model/predict the evolution and life cycle of a star based on certain initial conditions? That is, whether it will become a red giant, brown dwarf, etc. I'm basically looking for equations defining the progress of different star-types and how varying initial conditions may affect that progress.

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Please check out and see if it answers your question(s). If you still have gaps you should edit your question to make it more specific about what exactly you're looking for. – Brandon Enright May 8 '13 at 5:29

You could look at tools like EZ-web or interpolation formulae like those from Hurley, Pols and Tout 2000 to do so based on the initial mass and metallicity of your star. Here is a picture of the evolution of an initial 10 solar masses star and solar metallicity computed using Hurley's formulae (accessible as a fortran library, see this page for a web-interface)

a 10 solar masses star evolution within the HR diagram!

This one compares EZ results and Hurley's formulae.

EZ and Hursley's formulae comparison

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