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- catalog abstract "This book is about nonlinear dynamical systems and their bifurcations under parameter variation. It aims to provide 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. Basic results of bifurcation theory, such as Andronov-Hopf, planar homoclinic, period-doubling, and Neimark-Sacker bifurcations, are presented in much detail, including self-contained proofs not available in existing textbooks. Several recent results are also discussed, like generic two-parameter bifurcations of equilibria and fixed points, bifurcations of homoclinic orbits to non-hyperbolic equilibria, and one-parameter bifurcations of limit cycles in systems with reflectional symmetry, which are hardly covered in graduate-level textbooks. The presented material is sufficient to perform quite complex bifurcation analysis of dynamical systems and to understand basic methods, results, and terminology used in modern applied mathematics literature.".
- catalog contributor b8166249.
- catalog created "c1995.".
- catalog date "1995".
- catalog date "c1995.".
- catalog dateCopyrighted "c1995.".
- catalog description "1. Introduction to Dynamical Systems -- 2. Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems -- 3. One-Parameter Bifurcations of Equilibria in Continuous-Time Systems -- 4. One-Parameter Bifurcations of Fixed Points in Discrete-Time Systems -- 5. Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Systems -- 6. Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria -- 7. Other One-Parameter Bifurcations in Continuous-Time 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.".
- catalog description "Basic results of bifurcation theory, such as Andronov-Hopf, planar homoclinic, period-doubling, and Neimark-Sacker bifurcations, are presented in much detail, including self-contained proofs not available in existing textbooks. Several recent results are also discussed, like generic two-parameter bifurcations of equilibria and fixed points, bifurcations of homoclinic orbits to non-hyperbolic equilibria, and one-parameter bifurcations of limit cycles in systems with reflectional symmetry, which are hardly covered in graduate-level textbooks. The presented material is sufficient to perform quite complex bifurcation analysis of dynamical systems and to understand basic methods, results, and terminology used in modern applied mathematics literature.".
- catalog description "Includes bibliographical references (p. [487]-501) and index.".
- catalog description "This book is about nonlinear dynamical systems and their bifurcations under parameter variation. It aims to provide 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.".
- catalog extent "xv, 515 p. :".
- catalog hasFormat "Elements of applied bifurcation theory.".
- catalog identifier "0387944184 (acid-free paper)".
- catalog isFormatOf "Elements of applied bifurcation theory.".
- catalog isPartOf "Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 112.".
- catalog isPartOf "Applied mathematical sciences ; 112".
- catalog issued "1995".
- catalog issued "c1995.".
- catalog language "eng".
- catalog publisher "New York : Springer-Verlag,".
- catalog relation "Elements of applied bifurcation theory.".
- catalog subject "510 s 515/.352 20".
- catalog subject "Bifurcation theory.".
- catalog subject "QA1 .A647 vol. 112 QA380".
- catalog tableOfContents "1. Introduction to Dynamical Systems -- 2. Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems -- 3. One-Parameter Bifurcations of Equilibria in Continuous-Time Systems -- 4. One-Parameter Bifurcations of Fixed Points in Discrete-Time Systems -- 5. Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Systems -- 6. Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria -- 7. Other One-Parameter Bifurcations in Continuous-Time 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.".
- catalog title "Elements of applied bifurcation theory / Yuri A. Kuznetsov.".
- catalog type "text".