Dynamical Principles in Switching Networks
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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.
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