TY  - BOOK
AU  - Liebscher,Stefan
ED  - SpringerLink (Online service)
TI  - Bifurcation without Parameters
T2  - Lecture Notes in Mathematics,
SN  - 9783319107776
AV  - QA372 
U1  - 515.352 23
PY  - 2015///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Differential equations
KW  - Partial differential equations
KW  - Dynamics
KW  - Ergodic theory
KW  - Ordinary Differential Equations
KW  - Partial Differential Equations
KW  - Dynamical Systems and Ergodic Theory
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-10777-6
ER  -