I think the parts you're focusing on are a type of nutsedge. There may be some small zoysiagrass plants in there, but there aren't many. It looks like your zoysia didn't come up or fill in.
Bermudagrass is certainly aggressive and will move in wherever it has an opportunity. Personally, I think bermudagrass (even an unimproved common type) looks better than centipedegrass, so I wouldn't mind keeping the bermudagrass.
How has it taken hold? It could be a number of things, from seeds dispersed by wind or birds, to contaminated soil or sod, to a small patch of existing bermduagrass finally got enough sunlight and resources to take off.
But, now that it's here, you can encourage it by managing the entire lawn like bermduagrass. Centipedegrass is sensitive to some herbicides, so those could be used to weaken it. I would think you would want to make a slow and steady transition instead of all-at-once.