neuroscience - Can parts of a human brain be asleep independently of each other, or vary in the times required for them to fall asleep?

I know that some birds and marine animals can continue complicated activity (swimming, flying?) while one hemisphere of their brain is asleep.

I'm interested if human brain has some parts of it that can be asleep while others are awake? In other words, can a human brain be only partially asleep while experiencing insomnia or similar sleep disturbances?

If human brain can have different parts "sleeping" independently of each other, is it possible that the times to "fall asleep" vary between these different parts of the brain?

I would appreciate research articles on the topic or just the names of brain regions that may exhibit behavior described above.

Update: I've taken a look at R&K "principles and practice of sleep medicine"' and it mentions the following parts as involved in sleep:

Medulla, preoptic area, hypothalamus, thalamus, entire neocortex involved in NREM.

Neurotransmitter systems: histaminergic, orexinergic, serotonergic, noradrinergic

Sleep factors: adenosine, interleukin-1 and other cytokines, prostaglandin D2, growth hormone releasing hormone, nitric oxide, all promote sleep in or around preoptic area.

This makes me hypothesize that drugs that modify the effects of these systems (ex- caffeine affecting adenosine) could result in sleep- related disturbances in these systems, potentially causing them to fall asleep later that usual. But I'm looking for more info to fihre out if this is true