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" Elements of applied bifurcation theory / "
Yuri A. Kuznetsov.
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BL
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| Record Number
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849142
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| Main Entry
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Kuznet︠s︡ov, I︠U︡. A., (I︠U︡riĭ Aleksandrovich)
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| Title & Author
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Elements of applied bifurcation theory /\ Yuri A. Kuznetsov.
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| Edition Statement
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3rd ed.
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| Publication Statement
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New York :: Springer,, ©2004.
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| Series Statement
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Applied mathematical sciences ;; v. 112
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| Page. NO
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xxii, 631 pages :: illustrations ;; 24 cm
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| ISBN
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0387219064
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: 1441919511
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: 9780387219066
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: 9781441919519
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| Bibliographies/Indexes
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Includes bibliographical references (pages 599-618) and index.
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| Contents
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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 -- References -- Index.
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| Abstract
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"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 modern techniques for bifurcation analysis."--Pub. desc.
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| Subject
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Bifurcation theory.
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| Subject
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Bifurcation, Théorie de la.
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| Subject
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Bifurcation theory.
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| Subject
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Bifurcatie.
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Dynamische systemen.
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| Dewey Classification
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510 s515/.392
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515/.352
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| LC Classification
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QA1.A647 vol. 112 1998b
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| NLM classification
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31.44bcl
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31.44.bcl
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34C23msc
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37-04msc
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37Gxxmsc
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37M20msc
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