In this thesis I examine a delay differential equation model for an artificial neural network with two neurons. Linear stability analysis is used to determine the stability region of the stationary solutions. They can lose stability through either a pitchfork or a supercritical Hopf bifurcation. It is shown that, for appropriate parameter values, an interaction takes place between the pitchfork and Hopf bifurcations. Conditions are found under which the set of initial conditions that converge to a stable stationary solution is open and dense in the function space. Analytic results are illustrated with numerical simulations.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.23927 |
| Date | January 1995 |
| Creators | Olien, Leonard |
| Contributors | Belair, Jacques (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Mathematics and Statistics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001485361, proquestno: MM12253, Theses scanned by UMI/ProQuest. |
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