03694nam 22006975 450 991013231330332120200629194538.03-319-10777-110.1007/978-3-319-10777-6(CKB)3710000000306118(SSID)ssj0001386367(PQKBManifestationID)11814646(PQKBTitleCode)TC0001386367(PQKBWorkID)11368924(PQKB)10827146(DE-He213)978-3-319-10777-6(MiAaPQ)EBC6287894(MiAaPQ)EBC5610756(Au-PeEL)EBL5610756(OCoLC)898067286(PPN)183094344(EXLCZ)99371000000030611820141108d2015 u| 0engurnn|008mamaatxtccrBifurcation without Parameters /by Stefan Liebscher1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (XII, 142 p. 34 illus., 29 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;2117Bibliographic Level Mode of Issuance: Monograph3-319-10776-3 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.Lecture Notes in Mathematics,0075-8434 ;2117Differential equationsDifferential equations, PartialDynamicsErgodic theoryOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XDifferential equations.Differential equations, Partial.Dynamics.Ergodic theory.Ordinary Differential Equations.Partial Differential Equations.Dynamical Systems and Ergodic Theory.515.352Liebscher Stefanauthttp://id.loc.gov/vocabulary/relators/aut716388MiAaPQMiAaPQMiAaPQBOOK9910132313303321Bifurcation without parameters1388113UNINA