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The Hopf Bifurcation and Its Applications (Appl. Marsden<|
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Item specifics
- Condition
- PublishedOn
- 2013-10-04
- Title
- The Hopf Bifurcation and Its Applications (Applied Mathematical
- ISBN
- 9780387902005
- Publication Year
- 1976
- Type
- Textbook
- Format
- Paperback
- Language
- English
- Publication Name
- The Hopf Bifurcation and Its Applications
- Item Height
- 235mm
- Publisher
- Springer-Verlag New York Inc.
- Item Width
- 155mm
- Subject
- Mathematics
- Item Weight
- 1310g
- Number of Pages
- 408 Pages
About this product
Product Information
The goal of these notes is to give a reasonahly com plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations. Historical ly, the subject had its origins in the works of Poincare [1] around 1892 and was extensively discussed by Andronov and Witt [1] and their co-workers starting around 1930. Hopf's basic paper [1] appeared in 1942. Although the term Poincare Andronov-Hopf bifurcation is more accurate (sometimes Friedrichs is also included), the name Hopf Bifurcation seems more common, so we have used it. Hopf's crucial contribution was the extension from two dimensions to higher dimensions. The principal technique employed in the body of the text is that of invariant manifolds. The method of Ruelle Takens [1] is followed, with details, examples and proofs added. Several parts of the exposition in the main text come from papers of P. Chernoff, J. Dorroh, O. Lanford and F. Weissler to whom we are grateful. The general method of invariant manifolds is common in dynamical systems and in ordinary differential equations: see for example, Hale [1,2] and Hartman [1]. Of course, other methods are also available. In an attempt to keep the picture balanced, we have included samples of alternative approaches. Specifically, we have included a translation (by L. Howard and N. Kopell) of Hopf's original (and generally unavailable) paper.
Product Identifiers
Publisher
Springer-Verlag New York Inc.
ISBN-13
9780387902005
eBay Product ID (ePID)
89147698
Product Key Features
Publication Name
The Hopf Bifurcation and Its Applications
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
1976
Type
Textbook
Number of Pages
408 Pages
Dimensions
Item Height
235mm
Item Width
155mm
Volume
19
Item Weight
1310g
Additional Product Features
Series Title
Applied Mathematical Sciences
Country/Region of Manufacture
United States
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