During sleep, the brain undergoes dynamic and structural changes. In Drosophila, such changes have been observed in a brain area important both for sleep control and for navigation: the central complex. But in themselves, the two behaviors are largely disconnected processes. The connectivity of the central complex raises the question about how navigation, and specifically the head direction system, can operate in the face of sleep related plasticity. In this manuscript, theoretical modeling is used to describe the coupled dynamics of homeostatic sleep and navigation circuits. The authors can incorporate and explain several experimental findings about sleep and navigation both in flies and mice. Their model is based on a ring attractor network which is combined with plasticity rules that change between sleep and wake phases and shows autonomous dynamics during sleep, reminiscent of observations in the head direction system of mice.