Numerical Bifurcation Analysis of Maps
From Theory to Software

Combines a systematic analysis of bifurcations of iterated maps with concrete MATLAB® implementations and applications.

Yuri A. Kuznetsov (Author), Hil G. E. Meijer (Author)

9781108499675, Cambridge University Press

Hardback, published 28 March 2019

420 pages, 22 b/w illus. 136 colour illus. 16 tables
23.5 x 15.7 x 2.3 cm, 0.82 kg

'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 Review

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.

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.

Subject Areas: Maths for engineers [TBJ], Genetics [non-medical PSAK], Dynamics & statics [PHDT], Nonlinear science [PBWR], Mathematical modelling [PBWH], Numerical analysis [PBKS]