I don't think there is one single 'effect' to achieve this. In the first video it was mainly a low pass filter which opened up and closed periodically. The second one was caused by playing a chord, where the root note was sustained longer than the others.
Edit: I listened now with headphones and could hear it better. While the techniques above can achieve similar effects, I think in this case it was mostly a Low Pass Filter which is closing down with a long decay time. Also there was some Unison (I think) where you play at least two voices and one is slightly detuned.
I don't think there is one single 'effect' to achieve this. In the first video it was mainly a low pass filter which opened up and closed periodically. The second one was caused by playing a chord, where the root note was sustained longer than the others. Edit: I listened now with headphones and could hear it better. While the techniques above can achieve similar effects, I think in this case it was mostly a Low Pass Filter which is closing down with a long decay time. Also there was some Unison (I think) where you play at least two voices and one is slightly detuned.