Numerical bifurcation analysis of maps. From theory to software. (English) Zbl 1425.37002
Cambridge Monographs on Applied and Computational Mathematics 34. Cambridge: Cambridge University Press (ISBN 978-1-108-49967-5/hbk; 978-1-108-58580-4/ebook). xiv, 407 p. (2019).
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. It is divided into eleven chapters distributed in three parts.
Part 1 covers essentially all known theoretical results on bifurcations of maps, covering center manifold and normal form theory and codimension-one and -two bifurcations.
Part 2 covers software. In Chapter 5 numerical methods and algorithms are presented, while Chapter 6 discusses how these algorithms are implemented in the software package MatcontM. MatcontM is a software package written by the authors of this book which uses Matlab to perform bifurcation analysis of maps. Chapter 7 contains four tutorials on the use of MatcontM.
Part 3 contains four chapters, each devoted to the analysis of a particular map as a demonstration of the capabilities of MatcontM.
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.
Part 1 covers essentially all known theoretical results on bifurcations of maps, covering center manifold and normal form theory and codimension-one and -two bifurcations.
Part 2 covers software. In Chapter 5 numerical methods and algorithms are presented, while Chapter 6 discusses how these algorithms are implemented in the software package MatcontM. MatcontM is a software package written by the authors of this book which uses Matlab to perform bifurcation analysis of maps. Chapter 7 contains four tutorials on the use of MatcontM.
Part 3 contains four chapters, each devoted to the analysis of a particular map as a demonstration of the capabilities of MatcontM.
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.
Reviewer: Carlo Laing (Auckland)
MSC:
37-02 | Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory |
65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |
37Gxx | Local and nonlocal bifurcation theory for dynamical systems |
97N80 | Mathematical software, computer programs (educational aspects) |
39A28 | Bifurcation theory for difference equations |
37M20 | Computational methods for bifurcation problems in dynamical systems |