Need help again for plant ID

These red plants were just perfect when they were planted over 6 months ago. I was told that they are very manageable and mostly used as accents. But they have grown rather profusely and produced those white button flowers which may look attractive but can get overwhelmingly unruly. While the vertical growth can be solved by regular pruning, the horizontal growth is another thing. They have almost tripled the area size alloted for them and are invading the half moon garden.

Can you please ID these red plants? Are they what you call "invasive'? Is it better to just replace them?

Here's a close up of those red plants.
Thanks!

That looks like a type of Alternanthera brasiliana, Ruby Leaf Joy Weed.

http://www.hear.org/starr/images/species/?q=alternanthera+brasiliana&o=plants

http://davesgarden.com/guides/pf/go/32241/

well it may be invasive but it sure is pretty! :O)

Thanks for your feedback, Metro and Cindy!

They were trimmed and pruned back over a month ago and started growing those red leaves again...and here is how they look now.
I wish that they would just remain this way coz their button-like flowers sprout anywhere they landed...even their lanky stems. start new growth whenever they touch the ground, making them invasive indeed!

Just beautiful - you really have a way with landscaping and putting in the perfect gardens. I tmust be so nice to sit on that patio with a cold drink and all that eye candy...

Thanks, Braveheartsmom!

If you were a neighbor, we would have frequent girls chat in this patio after work in the evening, drinking wine while watching the stars and searching for constellations...:)