Elements of Applied Bifurcation Theory
This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special attention is given to e...
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| Müşterek Yazar: | |
| Materyal Türü: | Elektronik Ekitap |
| Dil: | İngilizce |
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Cham :
Springer International Publishing : Imprint: Springer,
2023.
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| Edisyon: | 4th ed. 2023. |
| Seri Bilgileri: | Applied Mathematical Sciences,
112 |
| Konular: | |
| Online Erişim: | https://doi.org/10.1007/978-3-031-22007-4 |
| Etiketler: |
Etiketle
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İçindekiler:
- 1 Introduction to Dynamical Systems
- 2 Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems
- 3 One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems
- 4 One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems
- 5 Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Dynamical Systems
- 6 Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria
- 7 Other One-Parameter Bifurcations in Continuous-Time Dynamical Systems
- 8 Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems
- 9 Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems
- 10 Numerical Analysis of Bifurcations
- A Basic Notions from Algebra, Analysis, and Geometry
- A.1 Algebra
- A.1.1 Matrices
- A.1.2 Vector spaces and linear transformations
- A.1.3 Eigenvectors and eigenvalues
- A.1.4 Invariant subspaces, generalized eigenvectors, and Jordan normal form
- A.1.5 FredholmAlternative Theorem
- A.1.6 Groups
- A.2 Analysis
- A.2.1 Implicit and Inverse Function Theorems
- A.2.2 Taylor expansion
- A.2.3 Metric, normed, and other spaces
- A.3 Geometry
- A.3.1 Sets
- A.3.2 Maps
- A.3.3 Manifolds
- References.