Biosphere that simulates sun and moon shifts
Sun and moon-faking devices exist. Not sure about 'biosphere'. I have personally observed one for honeybees, but that one was fairly crude(bees are dumb). It was just a big room with a hive stand in the middle and a series of fluorescent lights on the ceiling that turned on one after the other. The goal was to mess with bee circadian rhythms and see which genes became more or less expressed in their brains.

There's a slightly more sophisticated thing called a 'grow cabinet'. It has expensive lights to produce sun-spectrum light at direct sunlight intensity and humidity and temperature controls. Scientists use them for crop research when the weather is too random and unpredictable and absolute control is required.

I believe advanced versions simulate moonlight and angle of insolation, but that sort of thing is expensive.

I don't know of any full-sized biodomes with fake celestial objects. The cost of such a biodome would be prohibitive, and the experiments it enabled might be easier(certainly cheaper) to do in a smaller container.