Do cycles sync?

My life is my work and my work is my life, I help run a shop where I live and we are a pretty small operation, about half of our staff is women and we are all great friends. My period had been a little strange for the first couple months when we all first became close, later on I was able to figure out when mine was coming based on how the other girls were acting. If one had PMS the rest were soon to follow. We are all about 3-4 days off from each other. I didn't think that cycles could sync and it was a funny joke that people made when girls were both mad at the same thing. But now our cycle leader as I call her, she always starts first, is going on vacation in Mexico and has some how managed to keep her body bleeding for 2 1/2 weeks. My period is two weeks late, and so is the third party in our weird cycle pattern. I don't feel any different. I have had a lot of symptoms of PMS but they will just go away. I know I work a lot and that can stress me out and cause my period to be late but do periods really sync!? This is so weird, for 2 weeks we have all three been stuck in the same stage of our cycles just progressed for way longer than normal. Help! Lol