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Population Modeling with Delay Diffe...

Nelson, Shawna.

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Population Modeling with Delay Differential Equations.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Population Modeling with Delay Differential Equations./
Author:	Nelson, Shawna.
Description:	35 p.
Notes:	Source: Masters Abstracts International, Volume: 52-02.
Contained By:	Masters Abstracts International52-02(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1543944
ISBN:	9781303326653

Population Modeling with Delay Differential Equations.
Nelson, Shawna.

Population Modeling with Delay Differential Equations. - 35 p.

Source: Masters Abstracts International, Volume: 52-02.

Thesis (M.S.)--Rochester Institute of Technology, 2013.

We investigate a delay differential equation system version of a model designed to describe finite time population collapse. The most commonly utilized population models are presented, including their strengths, weaknesses and limitations. We introduce the Basener-Ross model, and implement the Hopf bifurcation test to identify whether there is a Hopf bifurcation in this system. We attempt to improve upon the Basener-Ross model (which uses ordinary differential equations) by introducing delay differential equations to account for the gestational period of humans. We utilize the singularity-removing transformation of the original Basener-Ross system for the delay differential equation system as well. The new system is shown to have a Hopf bifurcation. We also investigate how the bifurcation diagram of the original ODE model changes with the introduction of delays.

ISBN: 9781303326653Subjects--Topical Terms:

515831
Mathematics.

Population Modeling with Delay Differential Equations.
LDR:01703nam a2200277 4500 001 1960399
005 20140616133308.5
008 150210s2013 ||||||||||||||||| ||eng d
020 $a 9781303326653
035 $a (MiAaPQ)AAI1543944
035 $a AAI1543944
040 $a MiAaPQ $c MiAaPQ
100 1 $a Nelson, Shawna. $3 2096048
245 1 0 $a Population Modeling with Delay Differential Equations.
300 $a 35 p.
500 $a Source: Masters Abstracts International, Volume: 52-02.
500 $a Adviser: Tamas Wiandt.
502 $a Thesis (M.S.)--Rochester Institute of Technology, 2013.
520 $a We investigate a delay differential equation system version of a model designed to describe finite time population collapse. The most commonly utilized population models are presented, including their strengths, weaknesses and limitations. We introduce the Basener-Ross model, and implement the Hopf bifurcation test to identify whether there is a Hopf bifurcation in this system. We attempt to improve upon the Basener-Ross model (which uses ordinary differential equations) by introducing delay differential equations to account for the gestational period of humans. We utilize the singularity-removing transformation of the original Basener-Ross system for the delay differential equation system as well. The new system is shown to have a Hopf bifurcation. We also investigate how the bifurcation diagram of the original ODE model changes with the introduction of delays.
590 $a School code: 0465.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a Rochester Institute of Technology. $b Applied and Computational Mathematics. $3 2096049
773 0 $t Masters Abstracts International $g 52-02(E).
790 $a 0465
791 $a M.S.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1543944