PHASER: A Universal Simulator for Dynamical Systems
Built on Java Technology

Modules

by

Hüseyin Koçak
University of Miami,
Phaser Scientific Software LLC

for

Discrete Chaos, Second Edition, by Saber Elaydi

Below, you will find entry points to a collection of Phaser simulations specifically crafted for the textbook Discrete Chaos by S. Elaydi. Simulations are labeled in accordance with the numbering of the Sections in the textbook.

To run the simulations, you should first install a copy of Phaser on your local machine, either from the CDROM included with the textbook or from our Web site http://www.phaser.com. Then you can simply click on a Phaser simulation picture or a link to bring it to life.

To run and explore these simulations, no previous experience with PHASER is necessary. Appropriate PhaserTips and guidance will be provided as needed. However, if you are a new user of PHASER, you might like to browse the pdf document GettingStarted for an overview of the program and work through the Tutorials therein. Please write to us with your comments and questions at info@phaser.com

• Chapter 1: The Stability of One-Dimensional Maps
• 1.2 Maps vs. Difference Equations    
• 1.3 Maps vs. Differential Equations    
• 1.4 Linear Maps/Difference Equations    
• 1.5 Fixed (Equilibrium) Points    
• 1.6 Graphical Iteration and Stability    
• 1.7 Criteria for Stability    
• 1.8 Periodic Points and their Stability    
• 1.9 The Period-Doubling Route to Chaos    
• 1.10 Applications    
• Chapter 4: Stability of Two-Dimensional Maps
• 4.3 Fundamental Set of Solutions    
• 4.4 Second-Order Difference Equations    
• 4.5 Phase Space Diagrams    
• 4.6 Stability Notions    
• 4.7 Stability of Linear Systems    
• 4.8 The Trace-Determinant Plane    
• 4.9 Liapunov Functions for Nonlinear Maps    
• 4.11 Stability via Linearization    
• 4.12 Aplications