Bifurcation without Parameters
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.
1120137646
Bifurcation without Parameters
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.
49.99 In Stock
Bifurcation without Parameters

Bifurcation without Parameters

by Stefan Liebscher
Bifurcation without Parameters

Bifurcation without Parameters

by Stefan Liebscher

Paperback(2015)

$49.99 
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Overview

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.

Product Details

ISBN-13: 9783319107769
Publisher: Springer International Publishing
Publication date: 11/08/2014
Series: Lecture Notes in Mathematics , #2117
Edition description: 2015
Pages: 142
Product dimensions: 6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

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.

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