Spiking networks cannot work without inhibiting neurons

Given a spiking network of 5 neurons: a, b, c, d, e

[a, b, c] build a cluster or pattern, that fires together.
[c, d, e] build another cluster that fires together.

When a and b fire, c will be stimulated.
When d and e fire, c will also be stimulated.
(c is shared by both patterns)

When applying the hebbian learning rule and start to connect the neurons with 'what fires together wires together', this will lead to all neurons being interconnected soon. The distinction of both patterns gets lost.

What we need to not loose both pattern states are two additional inhibiting neurons:
i1 fires together with a and c or b and c and inhibits d and e.
i2 fires together with d and c or e and c and inhibits a and b.

In nature, these inhibiting neurons are probably the Stellate cells.

So the next step in computing artificial spiking networks is: Build a network that can distinguish between different patterns by automatically applying the hebbian learning rule and with using inhibiting neurons.