Was Jesus' power limited relative to the belief of others? Mark 6 4-6:
  
  4 Then Jesus said to them, “People everywhere give honor to a prophet,
  except in his own town, with his own people, or in his home.” 5 Jesus
  was not able to do any miracles there except the healing of some sick
  people by laying his hands on them. 6 He was surprised that the people
  there had no faith. Then he went to other villages in that area and
  taught.


Like above, there are several examples where He can't heal people because of their unbelief.

However, there is a difference: He won't vs. He cannot - heal someone because of their unbelief and this concept is usually overlooked.

Is there anyway to determine if His power was drained or weakened by others and what does that mean for a believer today? 

Does this mean my level of faith (or vice versa) is analogous to this phenomenon described above?

Here we see Jesus only recognizes and heals certain people based on their faith or to demonstrate God's will: Why does Jesus feel only certain people that come into physical contact with Him?

Any studies, papers, speeches on this?
It's not like it's a video game and He needs "faith power-ups". The idea of God being dependent on us is a a ridiculous heresy. 

From http://cicministry.org/commentary/issue3.htm


  Some claim that Jesus at least temporarily lost His deity. This cannot
  be true if Jesus is "I AM" as He claimed repeatedly in the Gospel of
  John, and if He is "the same yesterday and today, and forever" as
  Hebrews 13:8 asserts. If Jesus was not God at anytime and was
  therefore dependent on something or someone else to become God, then
  His "deity" would be contingent and not true deity. Such teachings
  must therefore be rejected as heretical. Jesus by His eternal nature
  does not and cannot cease to be God.


And there are plenty of easily found commentaries that explain this verse.  Like this one:

From Gill's Exposition of the Entire Bible found here: 


  And he could there do no mighty work,.... Or miracle; not that Christ
  had no power in himself to work miracles, though their unbelief and
  contempt of him were very great; but it was not fit and proper that he
  should do any there, since such were their prejudices against him: it
  is an usual way of speaking with the Hebrews, when either it is not
  "fit" and proper that a thing should be done, or they "will" not do
  it, to say it cannot be done; see Genesis 19:22; and even it is said
  of God himself, "So that the Lord could no longer bear, because of
  your evil doings"


Or The Geneva Study Bible

And he {d} could there do no mighty work, save that he laid his hands upon a few sick folk, and healed them.

(d) That is, he would not: for we need to have faith if we are going to receive the works of God.

All of the commentaries seem pretty united that it doesn't denot a lack of power, but that He simply would not. It's the same basic usage in saying "God cannot sin".

It's not the He does not possess the power to do so, but that it's completely against His nature to do so.