Hi CB,
It is an iterative system. I have run into a case where, after ~30 iterations, the next 8 iterations repeat over and over and over...
Graphing x, it is a waveform.
Anyway, the first x[t-1] is fixed. If I change it, the particular case that repeats ends up converging, but I have to think that this will result in other cases oscillating instead of converging.
y is a parabolic function that is determined at the start of the algorithm. x is used to determine what value of y is used. The goal is for the system to converge.
A little more description
x[-1] = 1.0;
m[-1] = 5.0;
y[-1] = parabolic_lookup_table(m[-1]);
Loop starting at time 0:
y[t] = parabolic_lookup_table(m[t-1]);
x[t] = x[t-1]*y[t] / (y[t-1] - y[t])
m[t] += x[t]
Thinking back to a controls class that I had in college, I am wondering if there is a way to quantify stability of the system.