A vast majority of life on Earth exists in an environment where resource availability and environmental conditions are temporally periodic. There is therefore an evolutionary advantage for organisms to partition behavior into certain times of day. Circadian rhythms, endogenous near-24 hour oscillations in gene expression, perform this task. These rhythms exert control over a large fraction of biological processes, and as such are implicated in a wide range of diseases, especially metabolic and mental disorders. Circadian rhythms are generated at a single-cell level through a complex set of interlocked genetic feedback loops. Individual components of the circadian network are considered "sloppy" due to stochastic noise, and it is only through the interaction of cellular oscillators at a network level that precise rhythms are generated. Medically treating or reverse-engineering this complicated genetic architecture necessitates mathematical understanding at multiple physical scales, from cells to tissue.

This thesis seeks to describe the complex dynamics and hierarchical organization of circadian rhythms in mammals through systems dynamics and mathematical approaches. The overarching theme of this work will be the interplay between stochasticity and synchronization in circadian rhythms. Stochastic noise and precise oscillation are not completely at odds, however. In this thesis, I first develop a model of the circadian oscillator which incorporates the core negative feedback loop and an important neuropeptide coupling pathway. I use this model to investigate claims about the roles of Cryptochrome isoforms within the core circadian clock, and show that despite seemingly-different roles, experimental data is consistent with a parallel role for Cryptochrome isoforms. Next, I present a method for inferring functional connections within the suprachiasmatic nucleus (SCN), the mammalian "master clock", and describe the network structure within the SCN. Finally, I examine growth and development of the SCN in utero..