Numerical Bifurcation Analysis of Maps

Yuri A. Kuznetsov is Professor of Numerical Bifurcation Methods at the University of Twente and Associate Professor at Utrecht University. He has made significant contributions to the theory of codimension two bifurcations of smooth ODEs and iterated maps. His recent work has focussed on efficient numerical continuation and normal form analysis of maps, ODEs and DDEs, and on applications of these methods in ecology, economics, engineering, and neuroscience. He is also the author of the widely-used text and reference Elements of Applied Bifurcation Theory (Springer-Verlag, 3rd ed., 2010). Hil G. E. Meijer is Assistant Professor at the University of Twente. He has extensive experience in numerical bifurcation theory and interdisciplinary applications such as modeling Parkinson's disease and epilepsy. He is a co-supervisor of the Matcont software project and has given numerous workshops on its use.

• 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.

'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