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| Author | : I︠U︡riĭ Aleksandrovich Kuznet︠s︡ov |
| Publisher | : Cambridge University Press |
| Total Pages | : 423 |
| Release | : 2019-03-28 |
| Genre | : Mathematics |
| ISBN | : 1108499678 |
Combines a systematic analysis of bifurcations of iterated maps with concrete MATLAB® implementations and applications.
| Author | : Yuri A. Kuznetsov |
| Publisher | : Cambridge University Press |
| Total Pages | : 424 |
| Release | : 2019-03-28 |
| Genre | : Mathematics |
| ISBN | : 1108695140 |
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.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 243 |
| Release | : 1979-01-01 |
| Genre | : Mathematics |
| ISBN | : 008087147X |
Bifurcation of Maps and Applications
| Author | : Bernd Krauskopf |
| Publisher | : Springer |
| Total Pages | : 399 |
| Release | : 2007-11-06 |
| Genre | : Science |
| ISBN | : 1402063563 |
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
| Author | : Dirk Roose |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 415 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9400906595 |
Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989
| Author | : Robert A. Meyers |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1885 |
| Release | : 2011-10-05 |
| Genre | : Mathematics |
| ISBN | : 1461418054 |
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
| Author | : Yuri Kuznetsov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 648 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475739788 |
Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
| Author | : Jeremy S. Hughes |
| Publisher | : |
| Total Pages | : 190 |
| Release | : 2010 |
| Genre | : Continuation methods |
| ISBN | : |
| Author | : KÜPPER |
| Publisher | : Springer-Verlag |
| Total Pages | : 582 |
| Release | : 2013-11-27 |
| Genre | : Science |
| ISBN | : 3034862563 |
| Author | : Gardini Laura |
| Publisher | : World Scientific |
| Total Pages | : 648 |
| Release | : 2019-05-28 |
| Genre | : Mathematics |
| ISBN | : 9811204713 |
The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.
