After Jelly bean I have noticed my phone is doing some strange things when the battery gets really low (less than 4%). When the battery is low and I plug it in to charge it, my battery will still decrease until it gets to 0% left, then the phone will switch back and forth between charging and being disconnected (even though it is still connected). It switches about once a second and continues this switching until the phone dies. Once the phone is dead, it charges up and acts normal when I turn it back on. It's totally bizarre, I don't have any charging problems when the phone is above 4% battery. Has anyone else experienced this?