Bifurcation without Parameters
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…
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- Full title :Bifurcation without Parameters / by Stefan Liebscher.
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.
Read More ↓Edition Statements
- Publication Date:2015.
Publication Statements
- Publisher(s):Imprint, Springer, Springer International Publishing
- Place of Publication:Cham
- Language:eng
- Publication Date:2015.
The Physical Object
- Description:1 online resource XII, 142 pages 34 illustrations, 29 illustrations in color. : : online resource
Edition Identifiers
- ISBN:9783319107776, 3319107771, 3319107763, 9783319107769
- DOI:10.1007/978-3-319-10777-6
- oclc:on1022006162
- LC Classification:QA372
- Dewey Decimal:515.352
Table of Contents
Introduction -- Methods & Concepts -- Cosymmetries -- Codimension One -- Transcritical Bifurcation -- Poincar´e-Andronov-Hopf Bifurcation -- Application: Decoupling in Networks -- Application: Oscillatory Profiles -- Codimension Two -- egenerate Transcritical Bifurcation -- egenerate Andronov-Hopf Bifurcation -- Bogdanov-Takens Bifurcation -- Zero-Hopf Bifurcation -- Double-Hopf Bifurcation -- Application: Cosmological Models -- Application: Planar Fluid Flow -- Beyond Codimension Two -- Codimension-One Manifolds of Equilibria -- Summary & Outlook.
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