Global Aspects of Homoclinic Bifurcations of Vector Fields
Author: Ale Jan Homburg
Publisher: American Mathematical Soc.
Published: 1996-01-01
Total Pages: 148
ISBN-13: 9780821863015
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Global Aspects of Homoclinic Bifurcations of Vector Fields
Author: Ale Jan Homburg
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 128
ISBN-13: 0821804413
DOWNLOAD EBOOK →In this book, the author investigates a class of smooth one parameter families of vector fields on some $n$-dimensional manifold, exhibiting a homoclinic bifurcation. That is, he considers generic families $x_\mu$, where $x_0$ has a distinguished hyperbolic singularity $p$ and a homoclinic orbit; an orbit converging to $p$ both for positive and negative time. It is assumed that this homoclinic orbit is of saddle-saddle type, characterized by the existence of well-defined directions along which it converges to the singularity $p$. The study is not confined to a small neighborhood of the homoclinic orbit. Instead, the position of the stable and unstable set of the homoclinic orbit is incorporated and it is shown that homoclinic bifurcations can lead to complicated bifurcations and dynamics, including phenomena like intermittency and annihilation of suspended horseshoes.
Elements of Applied Bifurcation Theory
Author: Yuri A. Kuznetsov
Publisher: Springer Nature
Published: 2023-04-18
Total Pages: 722
ISBN-13: 3031220072
DOWNLOAD EBOOK →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.
Elements of Applied Bifurcation Theory
Author: Yuri Kuznetsov
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 648
ISBN-13: 1475739788
DOWNLOAD EBOOK →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.
Difference Equations, Discrete Dynamical Systems and Applications
Author: Saber Elaydi
Publisher: Springer
Published: 2019-06-29
Total Pages: 382
ISBN-13: 3030200167
DOWNLOAD EBOOK →The book presents the proceedings of the 23rd International Conference on Difference Equations and Applications, ICDEA 2017, held at the West University of Timișoara, Romania, under the auspices of the International Society of Difference Equations (ISDE), July 24 - 28, 2017. It includes new and significant contributions in the field of difference equations, discrete dynamical systems and their applications in various sciences. Disseminating recent studies and related results and promoting advances, the book appeals to PhD students, researchers, educators and practitioners in the field.
Normal Forms and Bifurcation of Planar Vector Fields
Author: Shui-Nee Chow
Publisher: Cambridge University Press
Published: 1994-07-29
Total Pages: 482
ISBN-13: 0521372267
DOWNLOAD EBOOK →This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary.
Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems
Author: Bernold Fiedler
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 816
ISBN-13: 3642565891
DOWNLOAD EBOOK →Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Bifurcations
Author: Takashi Matsumoto
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 502
ISBN-13: 4431682430
DOWNLOAD EBOOK →Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, however, should not be too simple, otherwise nothing interesting can happen. Albert Einstein once said "as simple as pos sible, but no more" . One of the major reasons for the circuits discussed being simple is due to their piecewise-linear characteristics. Namely, the voltage current relationships are composed of several line segments which are easy to build. Piecewise-linearity also simplifies rigorous analysis in a drastic man ner. (2) The piecewise-linearity of the circuits has far reaching consequences.
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Author: John Guckenheimer
Publisher: Springer Science & Business Media
Published: 2013-11-21
Total Pages: 475
ISBN-13: 1461211409
DOWNLOAD EBOOK →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.
Introduction to Applied Nonlinear Dynamical Systems and Chaos
Author: Stephen Wiggins
Publisher: Springer Science & Business Media
Published: 2006-04-18
Total Pages: 860
ISBN-13: 0387217495
DOWNLOAD EBOOK →This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik
