Dynamical Principles in Switching Networks

Switching networks are a common model for biological systems, especially

for genetic transcription networks. Stuart Kaufman originally proposed

the usefulness of the Boolean framework, but much of the dynamical

features there are not realizable in a continuous analogue. We introduce the notion

of braid-like dynamics as a bridge between Boolean and continuous dynamics and

study its importance in the local dynamics of ring and ring-like networks. We discuss

a near-theorem on the global dynamics of general feedback networks, and in the final

chapter study the main ideas of this thesis in models of a yeast cell transcription network.