Equilibrium

If the net input to an IAC unit is held fixed the unit will eventually settle to an equilibrium point.

Set

a_i= 0 and solve for a_iassuming net_iis positive.

0 = (max - a_i) net_i - decay (a_i - rest)
decay a_i + net_i a_i = max net_i + decay rest
a_i = (max net_i + decay rest) / (decay + net_i)

Assuming max = 1 and rest = 0:

a_i = net_i / (decay + net_i)

a_i = (net_i / decay) / (net_i/decay +1)

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