Equilibrium

Set a_i = 0 and solve for a_i assuming net_i is 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)

or

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