Description 
1 online resource (xi, 401 pages) 
Series 
Applied mathematical sciences, 00665452 ; v. 181 

Applied mathematical sciences (SpringerVerlag New York Inc.) ; v. 181

Contents 
Introduction  Hopf Bifurcation and Normal Form Computation  Comparison of Methods for Computing Focus Values  Application (I)Hilbert's 16th Problem  Application (II)Practical Problems  Fundamental Theory of the Melnikov Function Method  Limit Cycle Bifurcations Near a Center  Limit Cycles Near a Homoclinic or Heteroclinic Loop  Finding More Limit Cycles Using Melnikov Functions  Limit Cycle Bifurcations in Equivariant Systems 
Summary 
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 
Analysis 
Mathematics 

Differentiable dynamical systems 

Computer software 

Dynamical Systems and Ergodic Theory 

Differential Equations 

Approximations and Expansions 

Ordinary Differential Equations 

Mathematical Software 

Nonlinear Dynamics 
Bibliography 
Includes bibliographical references and index 
Subject 
Limit cycles.


Nonlinear systems.


Mathematics  methods.


Nonlinear Dynamics.

Form 
Electronic book

Author 
Yu, Pei, 1947

LC no. 
2012936364 
ISBN 
1447129172 

1447129180 (electronic bk.) 

9781447129172 

9781447129189 (electronic bk.) 
