Numerical Bifurcation Analysis of Maps: From Theory to Software (Cambridge Monographs on Applied and Computational Mathematics, Series Number 34)

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 (R) 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. Cover......Page 1 Front Matter......Page 3 Numerical Bifurcation Analysis of Maps:From Theory to Software......Page 5 Copyright......Page 6 Dedication......Page 7 Contents......Page 9 Preface......Page 13 Part One: Theory......Page 17 1 Analytical Methods......Page 19 2 One-Parameter Bifurcations of Maps......Page 46 3 Two-Parameter Local Bifurcations of Maps......Page 66 4 Center Manifold Reduction for LocalBifurcations......Page 201 Part Two: Software......Page 233 5 Numerical Methods and Algorithms......Page 235 6 Features and Functionality of MatcontM......Page 259 7 MatcontM Tutorials......Page 274 Part Three: Applications......Page 335 8 The Generalized H ́enon Map......Page 337 9 Adaptive Control Map......Page 370 10 Duopoly Model of Kopel......Page 378 11 The SEIR Epidemic Model......Page 401 References......Page 405 Index......Page 416 This book combines a comprehensive treatment of bifurcations of discrete-time dynamical systems with concrete instruction on implementations and applications in the free MATLAB (R) software MatContM. While self-contained and suitable for independent study, it is also written with users in mind and will be an invaluable reference for practitioners.