Once all the foliage has dried up you should reduce your watering to no more than once a week, if that. Don't fertilize during this period either. Just tuck the pot in an out of the way spot until next spring, when it should burst into life again. For us, that's usually around april or may, but it varies in different regions.

Once you see signs of the first new shoots emerging in the spring, that is the time to repot it into some fresh soil (you can either divide up it or leave it in a clump) with a little fertilizer boost to get it off to a good start. We use a balanced slow-release type like Nutricote or Osmocote.

Even in it's native Thailand, which of course is super tropical, they go dormant in the winter.