Hi, I have been doing some experiments with phaser programs. I really like setting the feedback to really high levels, so that the phasor sounds really metallic and resonant, almost like a physical modeling instrument. 

The problem with this is it's easy to go overboard and get runaway feedback which gets harsh extremely quickly. 

I am wondering if there is a way to calculate the point at which self oscillation will occur given the number of phaser poles, the cutoff frequency of the allpass filters, and the feedback level.

The phasor I am using uses a variable number of 1 pole allpass filters in series defined by the equation:

y(n) = A * ( x(n) + y(n-1) ) - x(n-1)

where A = (1 - (PI * AllpassFreq / SampleRate)) / (1 + (PI * AllpassFreq / SampleRate))

Here is a signal flow diagram:

Ultimately what I am looking for is an equation I can use to calculate the following:

Given a phaser with x poles with y cutoff self oscillation will being at feedback level z

Can anyone recommend a good method or some resources I could use to figure this out?