I do not use Logic/Ableton but that might prove useful or not.
Midi are just information that need to be transformed into sound by a synthesizer.
Most (every?) virtual or real synth is fitted with one or several Low Frequency Oscillators (LFO). These are oscillators which are specially made to produce very low oscillations (usually from 0.1Hz to 50Hz approximately).
Frequency and amplitude of these oscillators, and on what they are acting (on the gain for instance, or the filter) can usually be controlled by MIDI Control Change (MIDI CC), even thought the number of the CC controlling these parameters is not standardized, so you can control them with a MIDI track with control changes automations.
So not complete answer as this depends on the synth you are using to translate you MIDI track to sound, but LFOs should be the ones to look at!