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Bifurcation without Parameters / by Stefan Liebscher.
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2379,2381-2383 2385,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Liebscher, Stefan, Author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 2117
- Language:
- English
- Subjects (All):
- Differential equations.
- Differential equations, Partial.
- Dynamics.
- Ergodic theory.
- Ordinary Differential Equations.
- Partial Differential Equations.
- Dynamical Systems and Ergodic Theory.
- Local Subjects:
- Ordinary Differential Equations.
- Partial Differential Equations.
- Dynamical Systems and Ergodic Theory.
- Physical Description:
- 1 online resource (XII, 142 p. 34 illus., 29 illus. in color.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2015.
- Language Note:
- English
- Summary:
- 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.
- 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.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-319-10777-1
- OCLC:
- 898067286
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