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Bifurcation without Parameters

Stefan Liebscher (Autor)

Buch | Softcover

XII, 142 Seiten

2014
Springer International Publishing (Verlag)
978-3-319-10776-9 (ISBN)

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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.

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.

Erscheint lt. Verlag	19.11.2014
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XII, 142 p. 34 illus., 29 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	248 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	34C23,34C20,34C37,37G99,35B32 • Bifurcation without parameters • Equilibria • Manifolds • nonlinear dynamical systems • Ordinary differential equations • Partial differential equations
ISBN-10	3-319-10776-3 / 3319107763
ISBN-13	978-3-319-10776-9 / 9783319107769
Zustand	Neuware