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Bifurcation without parameters

Liebscher, Stefan.

Bifurcation without parameters

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Bifurcation without parametersby 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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-10777-6
ISBN:	9783319107776 (electronic bk.)

Bifurcation without parameters
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:

185804
Bifurcation theory.

LC Class. No.: QA380

Dewey Class. No.: 515.392

Bifurcation without parameters
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505 0 $a 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.
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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