CHAOS, BIFURCATIONS AND SIMPLE DYNAMICAL MODELS
Subtitle: Reasons for Chaos Creation
Publisher: Lambert Academic Publishing
Published: 2010
Language: eng
Format: Paperback
Number of pages: 80
ISBN-13: 9783838384313
Description: Chaos is a complex and erratic behavior possible in very simple systems. In this book, the behavior of some simple dynamical systems is studied by constructing mathematical models. Investigations are made on the periodic orbits for continuous maps and idea of sensitive dependence on initial conditions. A small attempt is made to find out the reasons / unknown conditions for the production of chaos in a system. This is explained through simple dynamical models. Besides, another attempt is made to identify, algebraically simplest chaotic flow. These are the significance of this study - "Chaos, Bifurcations and simple dynamical Models". The result is proving that it is possible to find out the reasons / unknown conditions under which chaotic behavior exhibits in various systems. The importance of result is, why chaos is produced in various systems? - may be identified in future. We feel that this book will serve as a good survey for numerical analysis, chaos and bifurcation in some simple nonlinear dynamical systems. Also, it will act as a good guide for graduate student encounters with bifurcation and chaos.
Table of contents: title: 1. INTRODUCTION …………………………………. 1; title: 2. LOGISTIC MODEL ………………………………. 5; title: 3. THE FAMILY OF LOGISTIC MAPS; title: (ONE DIMENSIONAL) …………………………….13; title: 4. LYAPUNOV EXPONENTS ………………………..30; title: 5. JACOBIAN MATRIX ………………………………40; title: 6. TWO DIMENSIONAL MAPS ……………………...47; title: 7. SIMPLE DYNAMICAL MODELS ……………….. 62