what kind of plant is this?
the border plant is Lariope...it should get a small purple/lavender flower...good border plant....
the other I can not see the flower to tell you exactly, but it is some type of bulb. I bet if you dig in a small area around the base of the the bird bath, you will find small onion/shallot looking things. Many bulbs come out at different times of the year, some narcisis type bulbs, like it cooler. After they are established, which obviously yours are, they will even come up through snow if the conditions are right. There are some that won't come out for a couple of years, due to rainfall levels etc.
I would dig one up with a flower on it and take it to your local garden center, or if you could get a closer pic of the flower and attach it.
If you'd feel like to share some of those bulbs, you can dig up some and pass then on to your friends, or even transplant them to other areas of your yard as well. Most bulbs so closely grown, like to be thinned they would do fine either way.
hopes this helps...they may be crocus