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Elements of Applied Bifurcation Theory, Kuznetsov Yuri A.



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Автор: Kuznetsov Yuri A.
Название:  Elements of Applied Bifurcation Theory
Перевод названия: Юрий Кузнецов: Элементы прикладной теории бифуркаций
ISBN: 9780387219066
Издательство: Springer
Классификация:
ISBN-10: 0387219064
Обложка/Формат: Hardback
Страницы: 653
Вес: 1.096 кг.
Дата издания: 09.08.2004
Серия: Applied Mathematical Sciences
Язык: English
Издание: 3rd ed. 2004
Иллюстрации: 251 black & white illustrations, 251 black & white
Размер: 241 x 164 x 41
Читательская аудитория: Tertiary education (us: college)
Ссылка на Издательство: Link
Рейтинг:
Поставляется из: Германии
Дополнительное описание: Формат: 235x155
Илюстрации: 251
Круг читателей: Advanced undergraduate or graduate students in mathematics
Ключевые слова:
Язык: eng
Издание: 3rd ed.
Оглавление: Introduction to Dynamical Systems.- Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems.- One-Parameter Bifurcations of Equilibria in Continuous-Time Systems.- One-Parameter Bifurcations of Fixed Points in Discrete-Time Systems.- Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Systems.- Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria.- Other One-Parameter Bifurcations in Continuous-Time Systems.- Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems.- Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems.- Numerical Analysis of Bifurcations.- A: Basic Notions from Algebra, Analysis, and Geometry.- References.- Index.





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Описание: This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of non-linear problems with even order nondegenerate non-linearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for non-linear evolution equations, a new notion of bifurcation. With this new notion of bifurcation, many long-standing bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book.

In particular, applications are covered for a variety of PDEs from science and engineering, including the Kuramoto-Sivashinsky equation, the Cahn-Hillard equation, the Ginzburg-Landau equation, reactio -diffusion equations in biology and chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of non-linear dynamics for many problems in science linearised engineering.


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