Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Numerical Bifurcation Analysis of Maps
  • Cited by 53
Publisher:
Cambridge University Press
Online publication date:
March 2019
Print publication year:
2019
Online ISBN:
9781108585804
DOI:
https://doi.org/10.1017/9781108585804
Subjects:
Mathematics, Computational Science, Physics and Astronomy, Numerical Analysis and Computational Science, Nonlinear Science and Fluid Dynamics
Series:
Cambridge Monographs on Applied and Computational Mathematics (34)
Information

Book 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® 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

‘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 Source: 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 Source: 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 Source: SIAM Review

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
  • 1 - Analytical Methods
    pp 3-29
      • You have access
    • PDF
    • Export citation
References

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.