Camouzis / Ladas Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures

Erscheinungsjahr 2007
ISBN: 978-1-58488-766-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 576 Seiten

Extending and generalizing the results of rational equations, Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their periodic trichotomies. The book also provides numerous thought-provoking open problems and conjectures on the boundedness character, global stability, and periodic behavior of solutions of rational difference equations. After introducing several basic definitions and general results, the authors examine 135 special cases of rational difference equations that have only bounded solutions and the equations that have unbounded solutions in some range of their parameters. They then explore the seven known nonlinear periodic trichotomies of third order rational difference equations. The main part of the book presents the known results of each of the 225 special cases of third order rational difference equations. In addition, the appendices supply tables that feature important information on these cases as well as on the boundedness character of all fourth order rational difference equations. A Framework for Future Research The theory and techniques developed in this book to understand the dynamics of rational difference equations will be useful in analyzing the equations in any mathematical model that involves difference equations. Moreover, the stimulating conjectures will promote future investigations in this fascinating, yet surprisingly little known area of research.

Zielgruppe

Applied mathematicians, physicists, economists, engineers, and undergraduate and graduate students in difference equations.

Autoren/Hrsg.

Camouzis, Elias

Ladas, G.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

Preface
INTRODUCTION
Preliminaries
Definitions of Stability
Linearized Stability Analysis
Semicycle Analysis
A Comparison Result
Full Limiting Sequences
Convergence Theorems
Equations with Bounded Solutions
Some Straightforward Cases
The Second Order Rational Equation
Boundedness by Iteration
Boundedness of Special Cases
Existence of Unbounded Solutions
Unbounded Solutions
Period Trichotomies
Existence of Prime Period-Two Solutions
Period-Two Trichotomies
Period-Three Trichotomy
Period-Four Trichotomy
Period-Five Trichotomy
Period-Six Trichotomy
Known Results for Each of the 225 Special Cases
Equations
Appendices
Bibliography
Index
Each chapter contains an Introduction.