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Kicks and Maps A different Approach to Modeling Biological Systems

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Date Issued:
2015
Summary:
Modeling a biological systems, is a cyclic process which involves constructing a model from current theory and beliefs and then validating that model against the data. If the data does not match, qualitatively or quantitatively then there may be a problem with either our beliefs or the current theory. At the same time directly finding a model from the existing data would make generalizing results difficult. A considerable difficultly in this process is how to specify the model in the first place. There is a need to be practice which accounts for the growing use of mathematical and statistical methods. However, as a systems becomes more complex, standard mathematical approaches may not be sufficient. In the field of ecology, the standard techniques involve discrete maps, and continuous models such as ODE's. The intent of this work is to present the mathematics necessary to study hybrids of these two models, then consider two case studies. In first case we con sider a coral reef with continuous change, except in the presence of hurricanes. The results of the data are compared quantitatively and qualitatively with simulation results. For the second case we consider a model for rabies with a periodic birth pulse. Here the analysis is qualitative as we demonstrate the existence of a strange attractor by looking at the intersections of the stable and unstable manifold for the saddle point generating the attractor. For both cases studies the introduction of a discrete event into a continuous system is done via a Dirac Distribution or Measure.
Title: Kicks and Maps A different Approach to Modeling Biological Systems.
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Name(s): Ippolito, Stephen Anthony, author
Naudot, Vincent, Thesis advisor
Florida Atlantic University, Degree grantor
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2015
Date Issued: 2015
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 71 p.
Language(s): English
Summary: Modeling a biological systems, is a cyclic process which involves constructing a model from current theory and beliefs and then validating that model against the data. If the data does not match, qualitatively or quantitatively then there may be a problem with either our beliefs or the current theory. At the same time directly finding a model from the existing data would make generalizing results difficult. A considerable difficultly in this process is how to specify the model in the first place. There is a need to be practice which accounts for the growing use of mathematical and statistical methods. However, as a systems becomes more complex, standard mathematical approaches may not be sufficient. In the field of ecology, the standard techniques involve discrete maps, and continuous models such as ODE's. The intent of this work is to present the mathematics necessary to study hybrids of these two models, then consider two case studies. In first case we con sider a coral reef with continuous change, except in the presence of hurricanes. The results of the data are compared quantitatively and qualitatively with simulation results. For the second case we consider a model for rabies with a periodic birth pulse. Here the analysis is qualitative as we demonstrate the existence of a strange attractor by looking at the intersections of the stable and unstable manifold for the saddle point generating the attractor. For both cases studies the introduction of a discrete event into a continuous system is done via a Dirac Distribution or Measure.
Identifier: FA00004508 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2015.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Artificial intellligence -- Biological applications
Biology -- Mathematical models
Computational intelligence
Differential dynamical systems
Nonliner mechanics -- Mathematical models
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Links: http://purl.flvc.org/fau/fd/FA00004508
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00004508
Use and Reproduction: Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.