All biological systems require the functioning of both daylight and
darkness to survive in our world. What is the word that describes this
phenomena?

I don't know of a single word that would meet your description. The
terms "circadian rhythms," "diurnal rhythms," and "nyctohemeral
rhythms" are related to the phenomenon which you describe.

I've never seen the word 'scotobiology', nor can I find any references to it.

Photobiology?
http://lsvl.la.asu.edu/plb440/ltowill/text/bio464syll.html

The premise of your question may be true for some creatures, but
certainly not for all.

There are many forms of life that live in complete darkness in the
depths of the ocean, in caves, in the soil, etc.  They do quite nicely
in their niches, even in the total absence of daylight.

Chronobiology?
http://www.earlbakken.com/text.phtml?m=15

I'll take one final crack at this and suggest that you may be looking
'scotobiotic(s)' from the Greek scoto- (skoto) for 'darkness' and
biotics (biotikos) meaning the functions and qualities peculiar to
living organisms, or the sum of knowledge regarding these qualities.
(Dorland's 27th Ed.)

There is only a single reference on Vivisimo in a vocabulary section --
scotobiotic:  capable of thriving in darkness - scoto, (darkness).
http://www.megafoundation.org/UltraHIQ/HIQNews/S_Words.html

Additionally, there is a class of bacteria called Scotobacteria 
comprised of gram-negative organisms that do not derive energy from 
light (nonphototrophic metabolism).
http://www.ndif.org/Terms/Scotobacteria.html

The Biotic Message:
http://www1.minn.net/~science/index.html

Hope this is helpful to you,
V