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LARGE DEVIATIONS APPROACH TO THE BISTABLE
SYSTEMS WITH FRACTAL BOUNDARIES
by
Yu Zeng
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful
llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
December 2008
Copyright 2008 Yu Zeng
Object Description
| Title | Large deviations approach to the bistable systems with fractal boundaries |
| Author | Zeng, Yu |
| Author email | zengyu@usc.edu; zengyusc@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2008-06-02 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-09-14 |
| Advisor (committee chair) | Baxendale, Peter |
| Advisor (committee member) |
Arratia, Richard A. Sun, Fengzhu Z. |
| Abstract | In this thesis, we study the discrete time dynamical system on the unit interval by low intensity additive Gaussian noise. We consider systems where the underlying deterministic system has two stable fixed points, and use large deviations methods to study transitions from one basin of attraction to the other. We investigate transition time between the basins of two attractors, and the places where transitions most likely occur. It's the dynamical system with fractal boundaries between two basins that is of great interest to us. We estimate the expected exit time from the neighborhoods of such complicated boundaries. Finally it is shown, for the system with the specific underlying linear mapping, that we are able to compute the quasipotentials exactly. |
| Keyword | large deviations; bistable systems; fractal boundaries; gaussian noise; action function; quasipotential |
| 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-m1598 |
| Contributing entity | University of Southern California |
| Rights | Zeng, Yu |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@dots.usc.edu |
| Filename | etd-Zeng-2140 |
| Archival file | uscthesesreloadpub_Volume23/etd-Zeng-2140.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@dots.usc.edu |
| Full text | LARGE DEVIATIONS APPROACH TO THE BISTABLE SYSTEMS WITH FRACTAL BOUNDARIES by Yu Zeng A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) December 2008 Copyright 2008 Yu Zeng |
