Numerical Bifurcation Analysis of Maps : From Theory to Software (Cambridge Monographs on Applied and Computational Mathematics)

Kuznetsov, Yuri A./ Meijer, Hil G. E.

Cambridge University Press（2019/03発売）

• 製本 Hardcover:ハードカバー版／ページ数 420 p.
• 言語 ENG
• 商品コード 9781108499675
• DDC分類 515.392

Full 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.

Contents

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.