We discuss a class of models arising in the study of circadian rhythm and the properties of the matrix equations providing the bifurcation points for a wide parameter class. In particular, we prove that the five dimensional system studied in the cited work of Gonze, Halloy, and Goldbeter can have only a simple Hopf bifurcation.
"Notes on circadian rhythm." Topol. Methods Nonlinear Anal. 41 (2) 387 - 400, 2013.