1.

Record Nr.

UNINA9910132313303321

Autore

Liebscher Stefan

Titolo

Bifurcation without Parameters / / by Stefan Liebscher

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015

ISBN

3-319-10777-1

Edizione

[1st ed. 2015.]

Descrizione fisica

1 online resource (XII, 142 p. 34 illus., 29 illus. in color.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2117

Disciplina

515.352

Soggetti

Differential equations

Partial differential equations

Dynamics

Ergodic theory

Ordinary Differential Equations

Partial Differential Equations

Dynamical Systems and Ergodic Theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di contenuto

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.

Sommario/riassunto

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.