In order to model the diurnal variation of certain cell populations we study general one-type branching processes whose individuals reproduce in a manner that is influenced by time in a periodic fashion. A Malthusian growth rate is established as well as a periodically varying asymptotic composition, over ages e.g.
Peter Jagers. Olle Nerman. "Branching Processes in Periodically Varying Environment." Ann. Probab. 13 (1) 254 - 268, February, 1985. https://doi.org/10.1214/aop/1176993079