How to Play the Saxophone
Control your breathing

First, let's exhale. If you expel all your breath, your body becomes tense. If you then relax, breath will naturally flow back into your body. You can breathe without tensing a muscle anywhere in your body. This is how your body feels when you are breathing naturally. Remember this feeling.
Now, breathe in again. If you still have room for more breath, breathe in again. Does your entire body begin to move as it swells up? Now, try to take another breath.  Breathe in until you cannot breathe in any more.
Now, hold your breath for 2 or 3 seconds in that condition without using your hands. At this point, your breath would like to escape with all its might. Now, let's exhale. Your breath is expelled, but at this stage, you are not able to control the flow. Up to this point, you have rarely, if ever, inhaled to capacity, even when playing an instrument, and "breath control" is how well you control this.

(Reference: Yamaha Music Media; "Start playing better today (alto saxophone)," Shogo Sakaemura, editor)

To go up and down a hill with the same speed, one has to be careful on the down-hill side to avoid going too fast, and on the up-hill side, power is required to maintain the same speed. This can also be said of respiration, and at some point there is a change from one direction to the other.
Maintaining the speed of breathing requires a "support." The abdomen slowly becomes tense, but it is certainly trying not to force breath out. You must not try to control sound with your mouth.

(Reference: Yamaha Music Media; "Start playing better today (alto saxophone)," Shogo Sakaemura, editor)

Changing breathing