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Record Nr. |
UNINA9910132313303321 |
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Autore |
Liebscher Stefan |
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Titolo |
Bifurcation without Parameters / / by Stefan Liebscher |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
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ISBN |
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Edizione |
[1st ed. 2015.] |
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Descrizione fisica |
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1 online resource (XII, 142 p. 34 illus., 29 illus. in color.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 2117 |
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Disciplina |
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Soggetti |
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Differential equations |
Partial differential equations |
Dynamics |
Ergodic theory |
Ordinary Differential Equations |
Partial Differential Equations |
Dynamical Systems and Ergodic Theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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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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Sommario/riassunto |
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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 |
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