Numerical Bifurcation Analysis of Maps —— From Theory To Software

----- 地图的数值分支分析：从理论到软件

ISBN: 9781108695145 出版年：2019 页码：424 Yuri A Kuznetsov Cambridge University Press

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.