Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles PDF full book. Access full book title Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles by Maoan Han. Download full books in PDF and EPUB format.
Author: Maoan Han Publisher: Springer Science & Business Media ISBN: 1447129180 Category : Mathematics Languages : en Pages : 408
Book Description
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.
Author: Maoan Han Publisher: Springer Science & Business Media ISBN: 1447129180 Category : Mathematics Languages : en Pages : 408
Book Description
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.
Author: Yanqian Ye Publisher: American Mathematical Soc. ISBN: 9780821845189 Category : Mathematics Languages : en Pages : 452
Book Description
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.
Author: Andrei K. Abramian Publisher: Springer Nature ISBN: 303053006X Category : Science Languages : en Pages : 276
Book Description
This book commemorates the 60th birthday of Dr. Wim van Horssen, a specialist in nonlinear dynamic and wave processes in solids, fluids and structures. In honor of Dr. Horssen’s contributions to the field, it presents papers discussing topics such as the current problems of the theory of nonlinear dynamic processes in continua and structures; applications, including discrete and continuous dynamic models of structures and media; and problems of asymptotic approaches.
Author: V. Gaiko Publisher: Springer Science & Business Media ISBN: 9781402075711 Category : Mathematics Languages : en Pages : 210
Book Description
This volume is devoted to the qualitative investigation of two-dimensional polynomial dynamical systems and is aimed at solving Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles. The author presents a global bifurcation theory of such systems and suggests a new global approach to the study of limit cycle bifurcations. The obtained results can be applied to higher-dimensional dynamical systems and can be used for the global qualitative analysis of various mathematical models in mechanics, radioelectronics, in ecology and medicine. Audience: The book would be of interest to specialists in the field of qualitative theory of differential equations and bifurcation theory of dynamical systems. It would also be useful to senior level undergraduate students, postgraduate students, and specialists working in related fields of mathematics and applications.
Author: Mario Bernardo Publisher: Springer Science & Business Media ISBN: 1846287081 Category : Mathematics Languages : en Pages : 497
Book Description
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.
Author: Freddy Dumortier Publisher: Springer Science & Business Media ISBN: 3540329021 Category : Mathematics Languages : en Pages : 309
Book Description
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.
Author: Colin Christopher Publisher: Springer Science & Business Media ISBN: 3764384107 Category : Mathematics Languages : en Pages : 167
Book Description
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.
Author: Dingjun Luo Publisher: World Scientific ISBN: 9789810220945 Category : Science Languages : en Pages : 484
Book Description
Dynamical bifurcation theory is concerned with the changes that occur in the global structure of dynamical systems as parameters are varied. This book makes recent research in bifurcation theory of dynamical systems accessible to researchers interested in this subject. In particular, the relevant results obtained by Chinese mathematicians are introduced as well as some of the works of the authors which may not be widely known. The focus is on the analytic approach to the theory and methods of bifurcations. The book prepares graduate students for further study in this area, and it serves as a ready reference for researchers in nonlinear sciences and applied mathematics.
Author: Valery Romanovski Publisher: Springer Science & Business Media ISBN: 0817647279 Category : Mathematics Languages : en Pages : 336
Book Description
Using a computational algebra approach, this comprehensive text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The book gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. It contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography, making it a suitable graduate textbook as well as research reference.
Author: Maoan Han
Author: Maoan Han
Author: Yanqian Ye
Author: Andrei K. Abramian
Author: V. Gaiko
Author: Mario Bernardo
Author: Freddy Dumortier
Author: Colin Christopher
Author: Jean-Pierre Francoise
Author: Dingjun Luo
Author: Valery Romanovski