instead of changing the framerate all the time, what isnt the best way as your sketch gets less reactive you should only execute the code you want only every X frames...

like in this example, where the line in value is the mouseX value in this case.
and by using modulo % http://processing.org/reference/modulo.html
you can execute the change in rotation only every X frames whereby X will change by changing the mouseX value.



float rota;
void setup(){
size(500,500);
rectMode(CENTER);
}

void draw(){
 
background(0);
translate(width/2,height/2);


rotate(rota);
rect(0,0,200,200);

if(frameCount%(1+mouseX/50)==0){
rota+=0.1;
}

}

Thanks for your answer, I understand your code but the thing is that I have a gif animation and so I don't understand how I can make it go faster or slower using anything else than framerate. It doesn't need to rotate or do any other move than to fly (it's a flying bird), so I can't control it any other way than make the animation go faster or slower

rotation, movement, animations, it doesnt matter, you can control everything like that.
i dont know how your gif animation code looks like, but i am pretty sure you can control it the same way.
if you post it i will embed it to make it work.

I have tried adapting your code with my gif animation, with rotation to begin with even though it doesn't need to rotate. Your code works perfectly, but when I replace the rectangle with my animation, it turns around the center instead of turning round itself. You'll see it when you try this: 

ok, here is a working example where you can control the speed of the gif animation by the position of the mouse.
as further to the left it gets that slower it will play.

1. import gifAnimation.*;
   
   int frame = 0;
   
   
   PImage[] animation;
   Gif loopingGif;
   Gif nonLoopingGif;
   boolean pause = false;
   
   
   void setup(){
   size(500,500);
   
   
     println("gifAnimation " + Gif.version());
    // create the PImage array for the interactive display
     animation = Gif.getPImages(this, "00002708.gif");
    
   }
   
   void draw(){
    
   background(0);
      image(animation[(frame%animation.length)],width/2,height/2);
   
   if(frameCount%(1+mouseX/20)==0){
    frame++;
   }
   
   }