First of all, this applies only for the Legendary Birds of X&Y.
Second of all, I know that you can only really BATTLE AND CATCH them on that island, the Sea Spirit's Den.
What I want to know is HOW to catch up to them in the field. It seems that their movement patterns are MUCH different than before, including the likelihood that they just jump to another part of the map.
Also, how many times does one need to encounter them in the field before they run to the Sea Spirit's Den?