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...
সংরক্ষণ করুন:
| প্রধান লেখক: | |
|---|---|
| সংস্থা লেখক: | |
| বিন্যাস: | বৈদ্যুতিক বৈদ্যুতিন গ্রন্থ |
| ভাষা: | ইংরেজি |
| প্রকাশিত: |
Cham :
Springer International Publishing : Imprint: Springer,
2023.
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| সংস্করন: | 4th ed. 2023. |
| মালা: | Applied Mathematical Sciences,
112 |
| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | https://doi.org/10.1007/978-3-031-22007-4 |
| ট্যাগগুলো: |
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| 072 | 7 | |a GPFC |2 thema | |
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| 100 | 1 | |a Kuznetsov, Yuri A. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Elements of Applied Bifurcation Theory |h [electronic resource] / |c by Yuri A. Kuznetsov. |
| 250 | |a 4th ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XXVI, 703 p. 287 illus.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Applied Mathematical Sciences, |x 2196-968X ; |v 112 | |
| 505 | 0 | |a 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. | |
| 520 | |a 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 efficient numerical implementations of the developed techniques. Several examples from recent research papers are used as illustrations. The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the previous editions, while updating the context to incorporate recent theoretical and software developments and moderntechniques for bifurcation analysis. From reviews of earlier editions: "I know of no other book that so clearly explains the basic phenomena of bifurcation theory." - Math Reviews "The book is a fine addition to the dynamical systems literature. It is good to see, in our modern rush to quick publication, that we, as a mathematical community, still have time to bring together, and in such a readable and considered form, the important results on our subject." - Bulletin of the AMS "It is both a toolkit and a primer" - UK Nonlinear News "The material is presented in a systematic and very readable form. It covers recent developments in bifurcation theory, with special attention to efficient numerical implementations.” - Bulletin of the Belgian Mathematical Society . | ||
| 588 | |a Print version record. | ||
| 650 | 0 | |a Dynamical systems. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Mathematics. | |
| 650 | 1 | 4 | |a Dynamical Systems. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Applications of Mathematics. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031220067 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031220081 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031220098 |
| 830 | 0 | |a Applied Mathematical Sciences, |x 2196-968X ; |v 112 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-22007-4 |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||