Theory Of Limit Cycles

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Theory Of Limit Cycles

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Author : Yan-Qian Ye
language : en
Publisher: American Mathematical Soc.
Release Date :

Theory Of Limit Cycles written by Yan-Qian Ye and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

Over the past two decades the theory of limit cycles, especially for quadratic differential systems, has progressed dramatically in China as well as in other countries. This monograph, updating the 1964 first edition, includes these recent developments, as revised by eight of the author's colleagues in their own areas of expertise. The first part of the book deals with limit cycles of general plane stationary systems, including their existence, nonexistence, stability, and uniqueness. The second section discusses the global topological structure of limit cycles and phase-portraits of quadratic systems. Finally, the last section collects important results that could not be included under the subject matter of the previous two sections or that have appeared in the literature very recently. The book as a whole serves as a reference for college seniors, graduate students, and researchers in mathematics and physics.

Limit Cycles Of Differential Equations

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Author : Colin Christopher
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-16

Limit Cycles Of Differential Equations written by Colin Christopher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-16 with Mathematics categories.

This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Rechercha Mathematica Barcelona in 2006. It covers the center-focus problem for polynomial vector fields and the application of abelian integrals to limit cycle bifurcations. Both topics are related to the authors' interests in Hilbert's sixteenth problem, but would also be of interest to those working more generally in the qualitative theory of dynamical systems.

Theory Of Limit Cycles

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Author : Yanqian Ye
language : en
Publisher: American Mathematical Soc.
Release Date : 1986

Theory Of Limit Cycles written by Yanqian Ye and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.

Deals with limit cycles of general plane stationary systems, including their existence, nonexistence, stability, and uniqueness. This book also discusses the global topological structure of limit cycles and phase-portraits of quadratic systems.

Normal Forms Melnikov Functions And Bifurcations Of Limit Cycles

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Author : Maoan Han
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23

Normal Forms Melnikov Functions And Bifurcations Of Limit Cycles written by Maoan Han and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Mathematics categories.

Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.

Handbook Of Differential Equations Ordinary Differential Equations

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Author : A. Canada
language : en
Publisher: Elsevier
Release Date : 2006-08-21

Handbook Of Differential Equations Ordinary Differential Equations written by A. Canada and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-21 with Mathematics categories.

This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. - Covers a variety of problems in ordinary differential equations - Pure mathematical and real world applications - Written for mathematicians and scientists of many related fields

Qualitative Theory Of Differential Equations

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Author : Zhifen Zhang
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Qualitative Theory Of Differential Equations written by Zhifen Zhang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

Subriemannian geometries, also known as Carnot-Caratheodory geometries, can be viewed as limits of Riemannian geometries. They also arise in physical phenomenon involving ``geometric phases'' or holonomy. Very roughly speaking, a subriemannian geometry consists of a manifold endowed with a distribution (meaning a $k$-plane field, or subbundle of the tangent bundle), called horizontal together with an inner product on that distribution. If $k=n$, the dimension of the manifold, we get the usual Riemannian geometry. Given a subriemannian geometry, we can define the distance between two points just as in the Riemannian case, except we are only allowed to travel along the horizontal lines between two points. The book is devoted to the study of subriemannian geometries, their geodesics, and their applications. It starts with the simplest nontrivial example of a subriemannian geometry: the two-dimensional isoperimetric problem reformulated as a problem of finding subriemannian geodesics. Among topics discussed in other chapters of the first part of the book the author mentions an elementary exposition of Gromov's surprising idea to use subriemannian geometry for proving a theorem in discrete group theory and Cartan's method of equivalence applied to the problem of understanding invariants (diffeomorphism types) of distributions. There is also a chapter devoted to open problems. The second part of the book is devoted to applications of subriemannian geometry. In particular, the author describes in detail the following four physical problems: Berry's phase in quantum mechanics, the problem of a falling cat righting herself, that of a microorganism swimming, and a phase problem arising in the $N$-body problem. He shows that all these problems can be studied using the same underlying type of subriemannian geometry: that of a principal bundle endowed with $G$-invariant metrics. Reading the book requires introductory knowledge of differential geometry, and it can serve as a good introduction to this new, exciting area of mathematics. This book provides an introduction to and a comprehensive study of the qualitative theory of ordinary differential equations. It begins with fundamental theorems on existence, uniqueness, and initial conditions, and discusses basic principles in dynamical systems and Poincare-Bendixson theory. The authors present a careful analysis of solutions near critical points of linear and nonlinear planar systems and discuss indices of planar critical points. A very thorough study of limit cycles is given, including many results on quadratic systems and recent developments in China. Other topics included are: the critical point at infinity, harmonic solutions for periodic differential equations, systems of ordinary differential equations on the torus, and structural stability for systems on two-dimensional manifolds. This books is accessible to graduate students and advanced undergraduates and is also of interest to researchers in this area. Exercises are included at the end of each chapter.

Bifurcation Theory Of Limit Cycles

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Author : Han Mao'an
language : en
Publisher:
Release Date : 2016

Bifurcation Theory Of Limit Cycles written by Han Mao'an and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Bifurcation theory categories.

Bifurcation Theory And Spatio Temporal Pattern Formation

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Author : Wayne Nagata
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-10-03

Bifurcation Theory And Spatio Temporal Pattern Formation written by Wayne Nagata and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-03 with Mathematics categories.

Nonlinear dynamical systems and the formation of spatio-temporal patterns play an important role in current research on partial differential equations. This book contains articles on topics of current interest in applications of dynamical systems theory to problems of pattern formation in space and time. Topics covered include aspects of lattice dynamical systems, convection in fluid layers with large aspect ratios, mixed mode oscillations and canards, bacterial remediation of waste, gyroscopic systems, data clustering, and the second part of Hilbert's 16th problem. Most of the book consists of expository survey material, and so can serve as a source of convenient entry points to current research topics in nonlinear dynamics and pattern formation. This volume arose from a workshop held at the Fields Institute in December of 2003, honoring Professor William F. Langford's fundamental work on the occasion of his sixtieth birthday. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Essentials Of Nonlinear Control Theory

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Author : James R. Leigh
language : en
Publisher: IET
Release Date : 1983

Essentials Of Nonlinear Control Theory written by James R. Leigh and has been published by IET this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

The following topics are dealt with: nonlinearity: dynamic systems; describing function method; phase plane portrait; linearisation ;nonlinear second-order system linearisation; envelope methods; Limit cycles; relaxation oscillations; Lienard's equation; gradient systems and system decomposition.

Progress In Analysis

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Author : International Society for Analysis, Applications, and Computation. Congress
language : en
Publisher: World Scientific
Release Date : 2003-01-01

Progress In Analysis written by International Society for Analysis, Applications, and Computation. Congress and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.

The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting. Contents: .: Volume 1: Function Spaces and Fractional Calculus (V I Burenkov & S Samko); Asymptotic Decomposition (Methods of Small Parameters, Averaging Theory) (J A Dubinski); Integral Transforms and Applications (S Saitoh et al.); Analytic Functionals, Hyperfunctions and Generalized Functions (M Morimoto & H Komatsu); Geometric Function Theory (G Kohr & M Kohr); omplex Function Spaces (R Aulaskari & I Laine); Value Distribution Theory and Complex Dynamics (C C Yang); Clifford Analysis (K Grlebeck et al.); Octonions (T Dray & C Monogue); Nonlinear Potential Theory (O Martio); Classical and Fine Potential Theory, Holomorphic and Finely Holomorphic Functions (P Tamrazov); Differential Geometry and Control Theory for PDEs (B Gulliver et al.); Differential Geometry and Quantum Physics (-); Dynamical Systems (B Fiedler); Attractors for Partial Differential Equations (G Raugel); Spectral Theory of Differential Operators (B Vainberg); Pseudodifferential Operators, Quantization and Signal Analysis (M W Wong); Microlocal Analysis (B-W Schulze & M Korey); Volume 2: Complex and Functional Analytic Methods in PDEs (A Cialdea et al.); Geometric Properties of Solutions of PDEs (R Magnanini); Qualitative Properties of Solutions of Hyperbolic and SchrAdinger Equations (M Reissig & K Yagdjian); Homogenization Moving Boundaries and Porous Media (A Bourgeat & R P Gilbert); Constructive Methods in Applied Problems (P Krutitskii); Waves in Complex Media (R P Gilbert & A Wirgin); Nonlinear Waves (I Lasiecka & H Koch); Mathematical Analysis of Problems in Solid Mechanics (K Hackl & X Li); Direct and Inverse Scattering (L Fishman); Inverse Problems (G N Makrakis et al.); Mathematical Methods in Non-Destructive Evaluation and Non-Destructive Testing (A Wirgin); Numerical Methods for PDEs, Systems and Optimization (A Ben-Israel & I Herrera). Readership: Graduate students and researchers in real, complex, numerical analysis, as well as mathematical physics."