Dynamical Systems with Applications using Mathematica®

2007
ISBN: 978-0-8176-4482-6
Verlag: Birkhäuser

Buch, Englisch, 484 Seiten, Book, Format (B × H): 155 mm x 235 mm, Gewicht: 765 g

This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.

Zielgruppe

Research

Autoren/Hrsg.

Lynch, Stephen

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software

Inhaltsverzeichnis

Preface
A Tutorial Introduction to Mathematica
Differential Equations
Planar Systems
Interacting Species
Limit Cycles
Hamiltonian Systems, Lyapunov Functions, and Stability
Bifurcation Theory
Three-Dimensional Autonomous Systems and Chaos
Poincaré Maps and Nonautonomous Systems in the Plane
Local and Global Bifurcations
The Second Part of David Hilbert's Sixteenth Problem
Linear Discrete Dynamical Systems
Nonlinear Discrete Dynamical Systems
Complex Iterative Maps
Electromagnetic Waves and Optical Resonators
Fractals and Multifractals
Chaos Control and Synchronization
Neural Networks
Examination-Type Questions
Solutions to Exercises
References
Mathematica Program Index
Index