Graduation Year

2011

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

John G. Milton

Reader 2

Darryl Yong

Terms of Use & License Information

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 License

Rights Information

Austin Quan

Abstract

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential implications of this dynamical phenomenon to nocturnal frontal lobe epilepsy (NFLE) are also discussed.