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STABILITY OF A STOCHASTIC PREDATOR PREY MODEL
by
Joel H. Nibert
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2012
Copyright 2012 Joel H. Nibert
Object Description
| Title | Stability of a stochastic predator prey model |
| Author | Nibert, Joel H. |
| Author email | nibert@usc.edu;joel.nibert@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2012-06-25 |
| Date submitted | 2012-08-14 |
| Date approved | 2012-08-14 |
| Restricted until | 2012-08-14 |
| Date published | 2012-08-14 |
| Advisor (committee chair) | Baxendale, Peter |
| Advisor (committee member) |
Udwadia, Firdaus Lototsky, Sergey |
| Abstract | We consider a stochastic analog of the Lotka-Volterra model for the population dynamics of two interacting species, predator and prey. We investigate the long time behavior of the system, and show that, under certain conditions on the model parameters, asymptotic stability obtains. We provide a novel proof of the existing result of Rudnicki, emphasizing the use of the critical conditions. We split the first quadrant into regions, and through separate analyses, demonstrate that the predator prey process recurs to a compact set. Then a construction of Khasminskii and others provides for the existence of an invariant measure. |
| Keyword | predator-prey; stochastic differential equation; Lyapunov function; Lyapunov exponent; asymptotic stability; invariant measure |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Rights | Nibert, Joel H. |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume4/etd-NibertJoel-1156.pdf |
Description
| Title | Page 1 |
| Full text | STABILITY OF A STOCHASTIC PREDATOR PREY MODEL by Joel H. Nibert A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATHEMATICS) August 2012 Copyright 2012 Joel H. Nibert |
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