The darker purple ones (most common color, although they also come in lavender, wine, and pink) with the slightly larger flowers are called New England Aster, although their range is far greater than New England. The small light lavender ones are probably Calico Aster. The small white ones are so many species that look so similar that you would need a botanist to identify them. Asters are easy to propagate, you can dig up a clump, split it vertically with a knife or sharp shovel and replant the parts. Seed can be gathered, pressed into the soil, or very lightly covered. Do it this Fall, and Winter will stratify the seed as nature intended. Just don't expect flowers from seed the next year, it takes a year at minimum for the plant to gain enough size to bloom. Bees really go for the New England ones. Here is a great site with pictures of flowers and identifications, many apply to areas outside of Tennessee -
http://www.easttennesseewildflowers.comJC