Item Details

title

Noise-Induced Tipping in Networks of Neurons

author

Hofmann, Grace Elizabeth

abstract

A study of most probable transition paths for a piecewise linear, stochastic version of the Wilson-Cowan model – a model of excitatory and inhibitory neuron activity – is presented. Specifically, the Freidlin-Wentzell theory of large deviations is used to compute the most probable transition path by minimizing an appropriate rate functional. The novelty of this work stems from the fact that the underlying vector field of the system is piecewise linear and, thus, it is nontrivial to compute the solutions to the Euler-Lagrange equations. Instead, it is more tractable to construct the most probable transition path by evaluating the intersections of the invariant manifolds for the piecewise linear Hamiltonian system. This research has relevance in modeling disease that is linked to unbalanced excitatory and inhibitory neuron activity, i.e. autism, epilepsy, schizophrenia, etc.

contributor

Gemmer, John (advisor)

Robinson, Stephen (committee member)

Moore, Frank (committee member)

date

2023-01-24T09:35:50Z (accessioned)

2023-01-24T09:35:50Z (available)

2022 (issued)

degree

Mathematics (discipline)

identifier

http://hdl.handle.net/10339/101781 (uri)

language

en (iso)

publisher

Wake Forest University

type

Thesis