Bifurcations in the dynamical system and in the solutions of parameterized equations
Other Title(s)
التشعبات في الأنظمة الديناميكية و في حلول المعادلات ذات المعلمات
Dissertant
al-Hudaybiat, Bashir Muhammad Abd Allah
Thesis advisor
Comitee Members
Abu al-Shar, Musa Jabir
al-Khalid, Kamil Mustafa
Firasain, Basim Arif
University
Al albayt University
Faculty
Faculty of Sciences
Department
Department of Mathematics
University Country
Jordan
Degree
Master
Degree Date
2010
English Abstract
The study of bifurcations in dynamical system solutions (defined by differential equations or difference equations) is important subject that has applications in different fields of science including mathematics.
This thesis was studied the bifurcations and the status of the dynamical system around the fixed points.
The behavior of dynamical systems when the parameter changes and the bifurcations that occur as a result of the parameter change were also studied.
This work gathered all the theories and definitions required to study three important kinds of bifurcations: Pitchfork bifurcations, Tran critical bifurcations, and Saddle node bifurcations.
These kinds include examples of each and compare the conditions of their happenings.
The studied theories in this thesis were : the famous Sarkoviskii's theory, the implicit function theory, and Mores's Lemma which has helped in providing simple proof for the turning point theory, and reaches to proof of a pitchfork bifurcation theory.
Finally, this thesis was heavily depended upon the use of mathematical programming to draw the Cobweb diagram and the bifurcation phase plot.
The used programming software's Matlab 2010, Mathematic 6, Scientific Workplace 5.5, and Excel 2003.
These were proved to be helpful in identifying the exact solution to the differential and difference equation or to the root of polynomials.
Main Subjects
Topics
No. of Pages
94
Table of Contents
Table of contents.
Abstract.
Introduction.
Chapter One : preliminaries.
Chapter Two : bifurcation analysis.
Chapter Three : turning point theorem.
References.
American Psychological Association (APA)
al-Hudaybiat, Bashir Muhammad Abd Allah. (2010). Bifurcations in the dynamical system and in the solutions of parameterized equations. (Master's theses Theses and Dissertations Master). Al albayt University, Jordan
https://search.emarefa.net/detail/BIM-314844
Modern Language Association (MLA)
al-Hudaybiat, Bashir Muhammad Abd Allah. Bifurcations in the dynamical system and in the solutions of parameterized equations. (Master's theses Theses and Dissertations Master). Al albayt University. (2010).
https://search.emarefa.net/detail/BIM-314844
American Medical Association (AMA)
al-Hudaybiat, Bashir Muhammad Abd Allah. (2010). Bifurcations in the dynamical system and in the solutions of parameterized equations. (Master's theses Theses and Dissertations Master). Al albayt University, Jordan
https://search.emarefa.net/detail/BIM-314844
Language
English
Data Type
Arab Theses
Record ID
BIM-314844
