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Catalogue Information
Field name	Details
Dewey Class	515.39
Dewey Class	515.48
Title	Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles ([Ebook]) / by Maoan Han, Pei Yu.
Author	Han, Maoan
Added Personal Name	Yu, Pei
Other name(s)	SpringerLink (Online service)
Publication	London : Springer , 2012.
Physical Details	XI, 401 pages : 77 illus. : online resource.
Series	Applied mathematical sciences 0066-5452 ; ; 181
ISBN	9781447129189
Summary Note	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 focusÂ 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 onÂ the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbertâs 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.:
Contents note	Hopf Bifurcation and Normal Form Computation -- Comparison of Methods for Computing Focus Values -- Application (I)âHilbertâs 16th Problem -- Application (II)âPractical 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4471-2918-9
Links to Related Works	Subject References: Approximations and Expansions . Computer software . Differentiable dynamical systems . Differential equation . Dynamical systems and ergodic theory . Mathematical Software . Mathematics . Nonlinear Dynamics . Ordinary differential equations . Authors: author . Han, Maoan . Yu, Pei . Corporate Authors: SpringerLink (Online service) . Series: Applied mathematical sciences . Classification: 515.39 . 515.48 . 515.39 (DDC 23) .

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Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles

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