Bifurcation without parameters / Stefan Liebscher.
Material type:
TextSeries: Lecture notes in mathematics ; 2117.Publication details: Switzerland : Springer, 2015.Description: xii, 142 p. : illustrations ; 24 cmISBN: - 9783319107769
- 515.392 23 L717
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 515.392 L717 (Browse shelf(Opens below)) | Available | 135827 |
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| 515.392 Am518 Stabilization of elastic systems by collocated feedback / | 515.392 H752 Introduction to perturbation methods / | 515.392 K86 Optimization in function spaces | 515.392 L717 Bifurcation without parameters / | 515.392 N694 Nonlinear systems stability analysis : | 515.392 P332 Asymptotic analysis and perturbation theory / | 515.392 Sch326 Primer for chiral perturbation theory / |
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.
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