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Elements of Applied Bifurcation Theory

Author : Yuri Kuznetsov

Publisher : Springer Science & Business Media

Page : 648 pages

File Size : 26,47 MB

Release : 2013-03-09

Category : Mathematics

ISBN : 1475739788

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Book Description

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates 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 first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.



Dynamics and Bifurcations

Author : Jack K. Hale

Publisher : Springer Science & Business Media

Page : 577 pages

File Size : 29,38 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 1461244269

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Book Description

In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.



Global Bifurcations and Chaos

Author : Stephen Wiggins

Publisher : Springer Science & Business Media

Page : 505 pages

File Size : 13,30 MB

Release : 2013-11-27

Category : Mathematics

ISBN : 1461210429

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Book Description

Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.



Numerical Methods for Bifurcations of Dynamical Equilibria

Author : Willy J. F. Govaerts

Publisher : SIAM

Page : 384 pages

File Size : 44,86 MB

Release : 2000-01-01

Category : Mathematics

ISBN : 9780898719543

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Book Description

Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.



Bifurcations and Catastrophes

Author : Michel Demazure

Publisher : Springer Science & Business Media

Page : 304 pages

File Size : 14,93 MB

Release : 2013-06-29

Category : Mathematics

ISBN : 3642571344

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Book Description

Based on a lecture course, this text gives a rigorous introduction to nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach allowing a clear focus on the essential mathematical structures. It brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.



Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Author : Remco I. Leine

Publisher : Springer Science & Business Media

Page : 245 pages

File Size : 42,90 MB

Release : 2013-03-19

Category : Mathematics

ISBN : 3540443983

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Book Description

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.





Elements of Applied Bifurcation Theory

Author : Yuri A. Kuznetsov

Publisher : Springer Science & Business Media

Page : 529 pages

File Size : 17,93 MB

Release : 2013-03-09

Category : Mathematics

ISBN : 1475724217

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Book Description

A solid basis for anyone studying the dynamical systems theory, providing the necessary understanding of the approaches, methods, results and terminology used in the modern applied-mathematics literature. Covering the basic topics in the field, the text can be used in a course on nonlinear dynamical systems or system theory. Special attention is given to efficient numerical implementations of the developed techniques, illustrated by several examples from recent research papers. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used, making this book suitable for advanced undergraduate or graduate students in applied mathematics, as well as for researchers in other disciplines who use dynamical systems as model tools in their studies.



Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Author : John Guckenheimer

Publisher : Springer Science & Business Media

Page : 475 pages

File Size : 14,14 MB

Release : 2013-11-21

Category : Mathematics

ISBN : 1461211409

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Book Description

An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.



Bifurcation Theory

Author : Hansjörg Kielhöfer

Publisher : Springer Science & Business Media

Page : 355 pages

File Size : 49,15 MB

Release : 2006-04-10

Category : Mathematics

ISBN : 0387216332

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Book Description

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.