Date of Award
5-2011
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
First Thesis Advisor
John G. Milton
Second Thesis Advisor
Darryl Yong
Rights Information
Austin Quan
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 License
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.
Recommended Citation
Quan, Austin, "Noise, Delays, and Resonance in a Neural Network" (2011). HMC Senior Theses. Paper 24.
http://scholarship.claremont.edu/hmc_theses/24