LRT or LRT-like test on cyclical (Sleep) data
I think the problem is that you have time as a linear value rather than a factor. While this naively makes sense (after all, you have to go through 3 hours awake before you can get to 9 hours awake), what you end up doing is fitting a single coefficient to each gene of "linearly changes with time". What you want instead is factor, so you can have a system where things like per and clk can cycle:

time = factor(c(3,9,15,21))


The rest is then correct. Note that LRTs are not asking, "is there a change at any time point?", since there will likely be DE genes according to this that are not DE at any single time point. Rather an LRT such as this is asking, "What are genes that vary significantly over time?" There's a subtle different between those two questions. The former question is actually answered by a bunch of pairwise comparisons (taking the union of the DE genes).