Positive feedback equilibrium

[From Bruce Abbott (960115.2010 EST)]

Rick Marken (960115.1600) --

Me:

o := o + (k.2i-o)

Ye:

But doesn't this reduce to just

o := k.2i ?

Mathematically, yes. But with the replacement operation I think we just end
up adding an increment, k.2i-o, to o.

Well, let's take an example. Assume o := 10, k.2 = 2.0, i = 3. Then

  o := 10.0 + 2.0*3.0 - 10.0 = 2.0*3.0 = 6.0

Talk about leakage, this system leaks away _all_ of the previous amount of o
on each iteration. It can't work the way you describe. Are you sure you
didn't program:

  o := o + k.2*(i - o) ?

That is, does (k.2i+o) in your spreadsheet translate to the mathematical
function k2(i - o) rather than k2i + o?

Regards,

Bruce