Bifurcation without Parameters

• Main Author: Liebscher, Stefan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Lecture Notes in Mathematics, 2117
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Partial differential equations.; Ordinary Differential Equations.; Partial Differential Equations.; Dynamical Systems and Ergodic Theory.

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 c...

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.