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Bifurcation without parameters[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.392
書名/作者:	Bifurcation without parameters/ by Stefan Liebscher.
作者:	Liebscher, Stefan.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xii, 142 p. : : ill. (some col.), digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Bifurcation theory.
標題:	Manifolds (Mathematics)
標題:	Mathematics.
標題:	Ordinary Differential Equations.
標題:	Partial Differential Equations.
標題:	Dynamical Systems and Ergodic Theory.
ISBN:	9783319107776 (electronic bk.)
ISBN:	9783319107769 (paper)
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-10777-6

Bifurcation without parameters[electronic resource] /
Liebscher, Stefan.

Bifurcation without parameters[electronic resource] /by Stefan Liebscher. - Cham :Springer International Publishing :2015. - xii, 142 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,21170075-8434 ;. - Lecture notes in mathematics ;2035..

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 (electronic bk.)

Standard No.: 10.1007/978-3-319-10777-6doiSubjects--Topical Terms:

465718
Bifurcation theory.

LC Class. No.: QA380

Dewey Class. No.: 515.392

Bifurcation without parameters[electronic resource] /
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520 $a 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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