Topics In Bifurcation Theory And Applications 2nd Edition
Download Topics In Bifurcation Theory And Applications 2nd Edition PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Topics In Bifurcation Theory And Applications 2nd Edition book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Topics In Bifurcation Theory And Applications (2nd Edition)
Author: Moritz Adelmeyer
language: en
Publisher: World Scientific Publishing Company
Release Date: 1999-01-22
This textbook presents the most efficient analytical techniques in the local bifurcation theory of vector fields. It is centered on the theory of normal forms and its applications, including interaction with symmetries.The first part of the book reviews the center manifold reduction and introduces normal forms (with complete proofs). Basic bifurcations are studied together with bifurcations in the presence of symmetries. Special attention is given to examples with reversible vector fields, including the physical example given by the water waves. In this second edition, many problems with detailed solutions are added at the end of the first part (some systems being in infinite dimensions). The second part deals with the Couette-Taylor hydrodynamical stability problem, between concentric rotating cylinders. The spatial structure of various steady or unsteady solutions results directly from the analysis of the reduced system on a center manifold. In this part we also study bifurcations (simple here) from group orbits of solutions in an elementary way (avoiding heavy algebra). The third part analyzes bifurcations from time periodic solutions of autonomous vector fields. A normal form theory is developed, covering all cases, and emphasizing a partial Floquet reduction theory, which is applicable in infinite dimensions. Studies of period doubling as well as Arnold's resonance tongues are included in this part.
Topics in Bifurcation Theory and Applications
This textbook presents modern techniques of local bifurcation theory of vector fields. The first part reviews the Center Manifold theory and introduces a constructive approach of Normal Forms, with many examples. Basic bifurcations as saddle-node, pitchfork and Hopf are studied, together with bifurcations in the presence of symmetries. Special attention is given to examples with reversible vector fields. The second part deals with the Couette-Taylor hydrodynamical instability problem, between concentric rotating cylinders, when the rotation rates are varied. Primary bifurcations to Taylor-vortex flow, Spirals and Ribbons are studied, and secondary bifurcations are presented as illustrations of bifurcations from group orbits of solutions. The third part analyses bifurcations from periodic solutions, i.e. perturbations of an autonomous vector field having a closed orbit. Same tools are used, and studies of period doubling as well as Arnold's resonance tongues are included.
Elements of Applied Bifurcation Theory
Author: Yuri Kuznetsov
language: en
Publisher: Springer Science & Business Media
Release Date: 2004-06-29
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.