It's from Cuba. I haven't seen anything stating there is a dormancy. I believe it is actually an annual. Someone please correct me if I am wrong. Temperatures should never drop below 68F (20C). This will kill the plant. Apparently temps around 104F will cause the plant to multiple fairly quickly via clumps.
Edit: Perhaps not a true annual, but seems short lived in cultivation. Berry Rice's site states he kept his only for two years before it died.