Limit Cycles Of Differential Equations

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Limit Cycles of Differential Equations

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Author : Colin Christopher
Publisher : Springer Science & Business Media
ISBN 13 : 3764384107
Total Pages : 167 pages
Book Rating : 4.7/5 (643 download)

Book Synopsis Limit Cycles of Differential Equations by : Colin Christopher

Download or read book Limit Cycles of Differential Equations written by Colin Christopher and published by Springer Science & Business Media. This book was released on 2007-08-09 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : American Mathematical Soc.
ISBN 13 : 9780821845189
Total Pages : 452 pages
Book Rating : 4.8/5 (451 download)

Book Synopsis Theory of Limit Cycles by : Yanqian Ye

Download or read book Theory of Limit Cycles written by Yanqian Ye and published by American Mathematical Soc.. This book was released on 1986 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Notes on Diffy Qs

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Author : Jiri Lebl
Publisher :
ISBN 13 : 9781706230236
Total Pages : 468 pages
Book Rating : 4.2/5 (32 download)

Book Synopsis Notes on Diffy Qs by : Jiri Lebl

Download or read book Notes on Diffy Qs written by Jiri Lebl and published by . This book was released on 2019-11-13 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.

Differential Equations and Dynamical Systems

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Author : Lawrence Perko
Publisher : Springer Science & Business Media
ISBN 13 : 1468402498
Total Pages : 530 pages
Book Rating : 4.4/5 (684 download)

Book Synopsis Differential Equations and Dynamical Systems by : Lawrence Perko

Download or read book Differential Equations and Dynamical Systems written by Lawrence Perko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.

Differential Equations with Symbolic Computation

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Author : Dongming Wang
Publisher : Springer Science & Business Media
ISBN 13 : 3764374292
Total Pages : 374 pages
Book Rating : 4.7/5 (643 download)

Book Synopsis Differential Equations with Symbolic Computation by : Dongming Wang

Download or read book Differential Equations with Symbolic Computation written by Dongming Wang and published by Springer Science & Business Media. This book was released on 2006-03-16 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.

Limit-cycles in Averaged Ordinary Differential Equations

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Author : Peter Gross
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (246 download)

Book Synopsis Limit-cycles in Averaged Ordinary Differential Equations by : Peter Gross

Download or read book Limit-cycles in Averaged Ordinary Differential Equations written by Peter Gross and published by . This book was released on 1991 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Piecewise-smooth Dynamical Systems

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Author : Mario Bernardo
Publisher : Springer Science & Business Media
ISBN 13 : 1846287081
Total Pages : 497 pages
Book Rating : 4.8/5 (462 download)

Book Synopsis Piecewise-smooth Dynamical Systems by : Mario Bernardo

Download or read book Piecewise-smooth Dynamical Systems written by Mario Bernardo and published by Springer Science & Business Media. This book was released on 2008-01-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Study of Limit Cycles of an Autonomous System of Differential Equations

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Author : Roman Franciszek Matlak
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (216 download)

Book Synopsis Study of Limit Cycles of an Autonomous System of Differential Equations by : Roman Franciszek Matlak

Download or read book Study of Limit Cycles of an Autonomous System of Differential Equations written by Roman Franciszek Matlak and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finiteness Theorems for Limit Cycles

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Author : IU. S. Il'iashenko
Publisher : American Mathematical Soc.
ISBN 13 : 9780821845530
Total Pages : 342 pages
Book Rating : 4.8/5 (455 download)

Book Synopsis Finiteness Theorems for Limit Cycles by : IU. S. Il'iashenko

Download or read book Finiteness Theorems for Limit Cycles written by IU. S. Il'iashenko and published by American Mathematical Soc.. This book was released on 1991 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the following finiteness theorem: A polynomial vector field on the real plane has a finite number of limit cycles. To prove the theorem, it suffices to note that limit cycles cannot accumulate on a polycycle of an analytic vector field. This approach necessitates investigation of the monodromy transformation (also known as the Poincare return mapping or the first return mapping) corresponding to this cycle. To carry out this investigation, this book utilizes five sources: The theory of Dulac, use of the complex domain, resolution of singularities, the geometric theory of normal forms, and superexact asymptotic series. In the introduction, the author presents results about this problem that were known up to the writing of the present book, with full proofs (except in the case of the results in the local theory and theorems on resolution of singularities).

Existence of at Most Two Limit Cycles for the System of Differential Equations ...

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Author : Suo (Guangjian.)
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (651 download)

Book Synopsis Existence of at Most Two Limit Cycles for the System of Differential Equations ... by : Suo (Guangjian.)

Download or read book Existence of at Most Two Limit Cycles for the System of Differential Equations ... written by Suo (Guangjian.) and published by . This book was released on 1990 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles

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Author : Maoan Han
Publisher : Springer Science & Business Media
ISBN 13 : 1447129180
Total Pages : 408 pages
Book Rating : 4.4/5 (471 download)

Book Synopsis Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles by : Maoan Han

Download or read book Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles written by Maoan Han and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Qualitative Theory of Planar Differential Systems

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Author : Freddy Dumortier
Publisher : Springer Science & Business Media
ISBN 13 : 3540329021
Total Pages : 309 pages
Book Rating : 4.5/5 (43 download)

Book Synopsis Qualitative Theory of Planar Differential Systems by : Freddy Dumortier

Download or read book Qualitative Theory of Planar Differential Systems written by Freddy Dumortier and published by Springer Science & Business Media. This book was released on 2006-10-13 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.

Mat-report

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Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (912 download)

Book Synopsis Mat-report by :

Download or read book Mat-report written by and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Nonlinear Differential and Integral Equations

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Author : Harold Thayer Davis
Publisher :
ISBN 13 :
Total Pages : 590 pages
Book Rating : 4.:/5 (319 download)

Book Synopsis Introduction to Nonlinear Differential and Integral Equations by : Harold Thayer Davis

Download or read book Introduction to Nonlinear Differential and Integral Equations written by Harold Thayer Davis and published by . This book was released on 1960 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Dynamics and Chaos

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Author : Steven H. Strogatz
Publisher : CRC Press
ISBN 13 : 0429961111
Total Pages : 532 pages
Book Rating : 4.4/5 (299 download)

Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz

Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

A Second Course in Elementary Differential Equations

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Author : Paul Waltman
Publisher : Elsevier
ISBN 13 : 1483276600
Total Pages : 272 pages
Book Rating : 4.4/5 (832 download)

Book Synopsis A Second Course in Elementary Differential Equations by : Paul Waltman

Download or read book A Second Course in Elementary Differential Equations written by Paul Waltman and published by Elsevier. This book was released on 2014-05-10 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Second Course in Elementary Differential Equations deals with norms, metric spaces, completeness, inner products, and an asymptotic behavior in a natural setting for solving problems in differential equations. The book reviews linear algebra, constant coefficient case, repeated eigenvalues, and the employment of the Putzer algorithm for nondiagonalizable coefficient matrix. The text describes, in geometrical and in an intuitive approach, Liapunov stability, qualitative behavior, the phase plane concepts, polar coordinate techniques, limit cycles, the Poincaré-Bendixson theorem. The book explores, in an analytical procedure, the existence and uniqueness theorems, metric spaces, operators, contraction mapping theorem, and initial value problems. The contraction mapping theorem concerns operators that map a given metric space into itself, in which, where an element of the metric space M, an operator merely associates with it a unique element of M. The text also tackles inner products, orthogonality, bifurcation, as well as linear boundary value problems, (particularly the Sturm-Liouville problem). The book is intended for mathematics or physics students engaged in ordinary differential equations, and for biologists, engineers, economists, or chemists who need to master the prerequisites for a graduate course in mathematics.

On the Number of Limit Cycles for Some Families of Planar Differential Equations

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Author : Set Pérez-González
Publisher :
ISBN 13 : 9788449030765
Total Pages : 103 pages
Book Rating : 4.0/5 (37 download)

Book Synopsis On the Number of Limit Cycles for Some Families of Planar Differential Equations by : Set Pérez-González

Download or read book On the Number of Limit Cycles for Some Families of Planar Differential Equations written by Set Pérez-González and published by . This book was released on 2012 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: