عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
NATIONAL BIBLIOGRAPHY NUMBER
Number
TLpq2466761395
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Near-Pulse Solutions of the FitzHugh-Nagumo Equations on Cylindrical Surfaces
General Material Designation
[Thesis]
First Statement of Responsibility
Talidou, Afroditi
Subsequent Statement of Responsibility
Sigal, Israel Michael
.PUBLICATION, DISTRIBUTION, ETC
Name of Publisher, Distributor, etc.
University of Toronto (Canada)
Date of Publication, Distribution, etc.
2020
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
99
DISSERTATION (THESIS) NOTE
Dissertation or thesis details and type of degree
Ph.D.
Body granting the degree
University of Toronto (Canada)
Text preceding or following the note
2020
SUMMARY OR ABSTRACT
Text of Note
In 1961, FitzHugh suggested a model to explain the basic properties of excitability, namely the ability to respond to stimuli, as exhibited by the more complex Hodgkin-Huxley equations. The following year Nagumo et al. introduced another version based on FitzHugh's model. This is the model we consider herein. It is called the FitzHugh-Nagumo model and describes the propagation of electrical signals in nerve axons. Many features of the system have been studied in great detail in the case where an axon is modelled as a one-dimensional object. Here we consider a more realistic geometric structure: axons are modelled as warped cylinders and pulses propagate on their surface, closer to the reality of nature. The main results in this thesis are the stability of pulses for standard cylinders of small constant radius, and existence and stability of near-pulse solutions for warped cylinders whose radii are small and vary slowly along their lengths. On the standard cylinder, we write a solution near a pulse as the superposition of a modulated pulse with a fluctuation and prove that the fluctuation decreases exponentially over time as the solution converges to a nearby translation of the pulse. On warped cylinders we write a solution near a pulse in the same way as in standard cylinders and prove bounds on the fluctuation of near-pulse solutions.
TOPICAL NAME USED AS SUBJECT
Applied mathematics
Mathematics
PERSONAL NAME - PRIMARY RESPONSIBILITY
Sigal, Israel Michael
Talidou, Afroditi
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب p
[Thesis]
276903
a
Y
