Three problems in nonlinear dynamics -- delay equations, MEMS systems and infectious disease transmission

Other Titles
Abstract
In this doctoral dissertation we consider three problems in nonlinear dynamics -- a nonlinear second order delay differential equation (DDE), a nonlinear third order microelectromechanical (MEMS) system and a nonlinear first order DDE governing the spread of infectious diseases, in particular COVID-19. In the first problem, we consider the delayed Duffing equation $\ddot{x}+x_{d}+x^{3}=0$ where $x_d$ indicates delayed $x$. We find that as the delay is increased from zero, an infinite number of limit cycles of ever-increasing amplitude are born in a remarkable bifurcation. In the second problem, we construct a model of a MEMS cantilever which is heated by a laser. The model shows limit cycles. When two oscillators are coupled together, we get a very rich bifurcation sequence. The third problem relates to the spread of the pandemic COVID-19. We develop a model which is realistic and accounts for various features of the disease such as asymptomatic and latent (pre-symptomatic) transmission as well as interventions like contact tracing and mass testing.
Journal / Series
Volume & Issue
Description
102 pages
Sponsorship
Date Issued
2021-08
Publisher
Keywords
Location
Effective Date
Expiration Date
Sector
Employer
Union
Union Local
NAICS
Number of Workers
Committee Chair
Rand, Richard Herbert
Committee Co-Chair
Committee Member
Strogatz, Steven H.
Zehnder, Alan Taylor
Degree Discipline
Theoretical and Applied Mechanics
Degree Name
Ph. D., Theoretical and Applied Mechanics
Degree Level
Doctor of Philosophy
Related Version
Related DOI
Related To
Related Part
Based on Related Item
Has Other Format(s)
Part of Related Item
Related To
Related Publication(s)
Link(s) to Related Publication(s)
References
Link(s) to Reference(s)
Previously Published As
Government Document
ISBN
ISMN
ISSN
Other Identifiers
Rights
Attribution-NonCommercial 4.0 International
Types
dissertation or thesis
Accessibility Feature
Accessibility Hazard
Accessibility Summary
Link(s) to Catalog Record