Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Normal view MARC view ISBD view

Bifurcation without parameters / Stefan Liebscher.

By: Liebscher, Stefan.
Material type: TextTextSeries: Lecture notes in mathematics ; 2117.Publisher: Switzerland : Springer, 2015Description: xii, 142 p. : illustrations ; 24 cm.ISBN: 9783319107769.Subject(s): Bifurcation theory | Manifolds (Mathematics) | Ordinary Differential EquationsDDC classification: 515.392
Contents:
1. Introduction.- 2. Methods & Concepts.- 3. Cosymmetries.- 4. Transcritical Bifurcation.- 5. Poincar'e-Andronov-Hopf Bifurcation.- 6. Application: Decoupling in Networks.- 7. Application: Oscillatory Profiles.- 8. Degenerate Transcritical Bifurcation.- 9. Degenerate Andronov-Hopf Bifurcation.- 10. Bogdanov-Takens Bifurcation.- 11. Zero-Hopf Bifurcation.- 12. Double-Hopf Bifurcation.- 13. Application: Cosmological Models of binchi type, the tumbling universe.- 14. Application: Planar Fluid Flow in a planar channel, spatial dynamics with reversible bogdanov-takens bifurcation.- 15. Codimension-One Manifolds of Equilibria.- 16. Summary & Outlook.- References.
Summary: Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.
Tags from this library: No tags from this library for this title. Log in to add tags.
Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
515.392 L717 (Browse shelf) Available 135827
Total holds: 0

Includes bibliographical references.

1. Introduction.-
2. Methods & Concepts.-
3. Cosymmetries.-
4. Transcritical Bifurcation.-
5. Poincar'e-Andronov-Hopf Bifurcation.-
6. Application: Decoupling in Networks.-
7. Application: Oscillatory Profiles.-
8. Degenerate Transcritical Bifurcation.-
9. Degenerate Andronov-Hopf Bifurcation.-
10. Bogdanov-Takens Bifurcation.-
11. Zero-Hopf Bifurcation.-
12. Double-Hopf Bifurcation.-
13. Application: Cosmological Models of binchi type, the tumbling universe.-
14. Application: Planar Fluid Flow in a planar channel, spatial dynamics with reversible bogdanov-takens bifurcation.-
15. Codimension-One Manifolds of Equilibria.-
16. Summary & Outlook.-
References.

Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.

There are no comments for this item.

Log in to your account to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in


Visitor Counter