There is an invasion that, if you haven't seen it yet, is coming from our southern border. It looks friendly, can be a hard worker, but it is questionable as to whether it should be in our country. I don't know what you were thinking, but I am talking about Ruellia brittoniana (a.k.a. Mexican Petunia).
Mexican Petunia is native to Mexico, but it has escaped cultivation and has established itself in a great deal of the Southeastern U.S.
This is what mine looks like at the end of my sidewalk:
When I mentioned it has escaped cultivation, that is probably an understatement! According to the Florida Exotic Pest Council, Mexican Petunia is a Category 1 Invasive Plant. This means that it is "altering native plant communities by displacing native species, changing community structures or ecological functions, or hybridizing with natives". Where hardy, the Mexican petunia excels at invading wetlands, yards, fields, forests and anywhere else it can find soil.
Mexican petunia is a stalk forming perennial that stands up to 3 feet in height. Leaves are dark green, but the foliage will appear metallic blue/purple under full sun. They are 6-12 inches long and 1/2 to 3/4 of an inch wide. The blossoms are trumpet shaped and about 1.5-2 inches in diameter and are borne at the tips of the stems.
It likes fertile soil that is moist. Mexican Petunia is a water plant that becomes very aggressive with access to abundant moisture. It will survive dry spells once established however. I mentioned that it likes full sun, but will do well in partial shade. The quantity of blossoms is related to the amount of light the plant receives. The more direct sunlight the more flowers. You will actually get fewer flowers appearing on overcast days or when grown in shadier conditions. There are numerous varieties with a plethora of colors to choose from Purple, White, Pink, and many shades of Blue.
Here is a picture of a Pink one I found:
The reason this thing is considered an invasive plant is because of how easy it is to propagate. The running joke is, if you break off a piece, lay it on the sidewalk, it will root! If you have a friend growing it, ask to break off a piece or two, you only need a piece about 2 inches long to root. Other characteristics that make Mexican Petunia a successful invasive plant is its rapid growth rate, Mexican Petunia will resprout from crowns or rootstocks when cut back or killed back by frost. Mine die back every year and you see how big it is.
It is typically not bothered by any pest or disease.
Use Mexican Petunia towards the back of a flowering border, or as the centerpiece in a container. Butterflies and Bees love the flowers. It blooms enthusiastically throughout the hottest time of the year. It is usually inexpensive and sold in many big box stores.
There is a dwarf variety available, it is suppose to only get about a foot tall. All of the attributes of the full size one, only in miniature. I have not seen it myself, but it is out there.
I have had no real problem with my Ruellia, but I also keep mine in containers. I see shoots coming out from around the pot occasionally, but my lawnmower or weedwhacker seems to make quick work of them.
I have had many conversations with people about invasive plants. Yes, I can see where, if this thing really was allowed to grow, it could take over the world. Marigolds can do the same thing! I have never seen my Mexican Petunia produce seeds, the shoots are removed easily, and it doesn't borrow the car keys to go over to the next county. If you keep it in control, there should be no problem in growing this very pretty, fast growing plant.