I finally had time to read Mystran's suggested chapters from Vadim's book. It took several evenings to go through the texts and to digest their content properly. It was worth it. I intend to continue reading rest of the book.
So far I've derived the 1 pole and SVF filters (without non-linearities). I also used matt42's graph to derive my own "2 poles only" filter. All the mentioned filters seem to self-oscillate nicely with sweeping frequencies when a single impulse is fed into the filter. They also seem to behave rather nicely with high frequency modulation.
All this hype about trapezoidal integrators brings a question to my mind:
Has anyone tried using Simpson's integrators for ZDF filters?
Is there a reason no-one has even mentioned them?
One would imagine they would give even better behaving results...?
Feedback on Vadim's book:
Clearly the hardest parts to follow were the first 10 pages. Even though I had already read 2 books on DSP and understood them, these first 10 pages took lots of re-reading before I slowly realized that I already knew the information it was trying to convey. After that it quickly became easier and easier to understand. My suggestion is to rewrite and expand the first 10 pages so they're easier to follow. This way the audience for the book becomes magnitudes larger.
A few times when the book referred to some graph/formula, it had been introduced long ago in the book, tons of pages ago. Browsing the book so far away, trying to find the required graphs, is quite cumbersome. It might be a good idea to re-introduce some of those graphs/formulas again where they're referred to if more than X pages has gone since they were last seen.
Otherwise it has been an interesting book to read. Good job!