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Bifurcation without Parameters
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SpringerLink (Online service)
Bifurcation without Parameters
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Bifurcation without Parameters/ by Stefan Liebscher.
作者:
Liebscher, Stefan.
面頁冊數:
XII, 142 p. 34 illus., 29 illus. in color.online resource. :
Contained By:
Springer Nature eBook
標題:
Differential equations. -
電子資源:
https://doi.org/10.1007/978-3-319-10777-6
ISBN:
9783319107776
Bifurcation without Parameters
Liebscher, Stefan.
Bifurcation without Parameters
[electronic resource] /by Stefan Liebscher. - 1st ed. 2015. - XII, 142 p. 34 illus., 29 illus. in color.online resource. - Lecture Notes in Mathematics,21170075-8434 ;. - Lecture Notes in Mathematics,2144.
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.
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.
ISBN: 9783319107776
Standard No.: 10.1007/978-3-319-10777-6doiSubjects--Topical Terms:
527664
Differential equations.
LC Class. No.: QA372
Dewey Class. No.: 515.352
Bifurcation without Parameters
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