I noticed the samething with 1 of my dwarf platys. She is the bigger of the 3 and chases and nips at my other fish. It happens when my tank light comes on which they know means feeding time. I'm guessing it has to do with feeding in my case. She nips at their fins and body but I don't notice any damage at all. I use to be concerned about it but now it's just a normal routine. I guess it's harmless.
Check out my 2nd video (with light on) and you will notice my male guppy being chased by the female platy--->
My 15 Gallon Community Aquarium (2 Videos)