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Virginia Tech

Nonsmooth Bifurcations and the Role of Density Dependence in a Chaotic Infectious Disease Model

Abstract

dc:description.abstract

Discrete dynamical systems can exhibit rich and interesting dynamics at lower dimensions (and co-dimensions) than that of ODE models. Classically, the minimal dimension to observe chaotic behavior in an ODE model is three; whereas it can be achieved in a one-dimensional discrete map. It is often the choice of mathematical biologists to use discrete systems as it fills many roles such as sparse data, incorporation of life cycle stages and noisy measurements. This work is analyzes a discrete time model of an infected salmon population. It provides an in-depth analysis of non-smooth bifurcations for alternate functional forms for density dependence in the growth function of a given model. These demonstrate interesting structures and chaotic behaviors with biologically feasible interpretations such as intrinsic growth rate and probability of death. The choice of density dependence function, as well as parameterization, leads to whether chaos occurs or not.

Degree

thesis:*
Name thesis:degree_name
Master of Science
Level thesis:degree_level
masters
Discipline thesis:degree_discipline
Mathematics
Department dc:contributor.department
Mathematics
Grantor dc:publisher
Virginia Tech
Year dc:date.issued
2020

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Hughes, Ryan Patrick
Chair dc:contributor.committeechair
  • Childs, Lauren M.
Committee members dc:contributor.committeemember
  • Blackwood, Julie C.
  • Ciupe, Stanca M.

Subjects

dc:subject × 3

Rights

dc:rights
Statement dc:rights
  • In Copyright

Identifiers

dc:identifier.*
Dc Identifier Other
vt_gsexam:23713
OAI identifier oai:identifier
oai:vtechworks.lib.vt.edu:10919/96567

Chain of custody

source
Harvested from
Virginia Tech
Base URL
vtechworks.lib.vt.edu/oai/request
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
citation

Hughes, Ryan Patrick. Nonsmooth Bifurcations and the Role of Density Dependence in a Chaotic Infectious Disease Model. masters thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/96567