(...) between the dificulty increase and a possible influence on the BTC price.
How would difficulty have an influence on BTC price? You got it the wrong way 'round, man. Price determines difficulty.
Also, the amount of BTC available to exchanges is based on production rate, and difficulty adapts to
keep that constant. Miners might as well be Satoshi secretly writing magical BTC bucks with his quantum computer, the market would not change as long as the effective minting rate does not change.
Edit: oh, @topic: please use the word "stable" when more than two months have passed. Normal people will shake their head when one says "stable" because the market didn't explode in antimatter fireworks for a day.