Numerical Bifurcation Analysis of Maps
From Theory to Software
Published on 20. March 2019
424 pages
978-1-108-69514-5 (ISBN)
Description
This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB (R) software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze more complicated models from modern engineering, ecology, and economics.
Reviews / Votes
'The topic of this book is the study of local and global bifurcations (qualitative changes in dynamics) of discrete-time maps as parameters are varied ... This book could be used as reference to known results on bifurcations of maps, or as a guide to the software MatcontM. It is clearly written and contains many high-quality figures.' Carlo Laing, zbMATH 'Throughout the whole work, there is an abundance of joyfully complex figures depicting various dynamics via phase portrait sketches and bifurcation structures in parameter space ... The first half of this book will doubtless be an essential and convenient reference for specialists who already conduct research in this field.' Gavin M. Abernethy, LMS Newsletter 'This book is an excellent compendium of bifurcation results and phenomenology for low-dimensional maps, and would find itself usefully ensconced on the bookshelf next to the computer (running its accompanying software) of any researcher studying dynamical systems.' James Meiss, SIAM ReviewMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 16 Tables, black and white; 74 Halftones, color; 11 Halftones, black and white; 62 Line drawings, color; 11 Line drawings, black and white
File size
19,99 MB
ISBN-13
978-1-108-69514-5 (9781108695145)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
03/2019
Cambridge University Press
€204.90
Shipment within 15-20 days
Persons
Content
Part I. Theory: 1. Analytical methods; 2. One-parameter bifurcations of maps; 3. Two-parameter local bifurcations of maps; 4. Center-manifold reduction for local bifurcations; Part II. Software: 5. Numerical methods and algorithms; 6. Features and functionality of MatContM; 7. MatContM tutorials; Part III. Applications: 8. Examples; References; Index.
