Discrete Dynamics: Basic Theory and Examples

This book provides a comprehensive introduction to discrete dynamical systems, focusing on stability, fixed points, and periodic orbits. It offers a solid mathematical foundation and discusses topics often neglected in the research literature, including a comparison between discrete and continuous time models. Numerous examples, numerical simulations, and figures are included to demonstrate the flexibility and potential of the discrete approach. It serves as a reference material for courses at a doctoral or upper undergraduate level in mathematics and theoretical engineering.

Format: Paperback / softback
Length: 142 pages
Publication date: 04 March 2023
Publisher: Springer Nature Switzerland AG

This comprehensive and intricate book delves into the realm of discrete dynamical systems, providing a thorough and detailed introduction to the field. With a particular focus on the stability of fixed points and periodic orbits, it offers a solid mathematical foundation and essential basic knowledge for further advancements, such as deterministic chaos theory. Additionally, the book addresses topics that may be overlooked in the research literature, such as comparing different predictions achievable by the discrete time model and the continuous time model of the same application.

A novel aspect of this work is an accurate analysis of the mechanisms by which a fixed point can lose stability, introducing and comparing various notions of instability: simple instability, repulsivity, and complete instability. To aid the reader and showcase the versatility and potential of the discrete approach to dynamics, numerous examples, numerical simulations, and figures have been included. This book serves as a valuable reference material for courses at the doctoral or upper undergraduate level in mathematics and theoretical engineering.

Weight: 258g
Dimension: 234 x 156 x 14 (mm)
ISBN-13: 9783030950941
Edition number: 1st ed. 2022