connections['XeAe'] = sim.Projection(input_groups['e'], neuron_groups['e'], sim.OneToOneConnector(),sim.StaticSynapse(weight=1))
Brian considers the value of "1" as "1 s" while PyNN takes it as "1 ms" as is their normal convention.
Setting a strength of "1 s" might be too high a value. So we suggest you set it to a lower value.
Also, do verify that your neuron equations are correct.
Cheers.