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.

‘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