The Resource Normal forms, melnikov functions and bifurcations of limit cycles, Maoan Han, Pei Yu
Normal forms, melnikov functions and bifurcations of limit cycles, Maoan Han, Pei Yu
Resource Information
The item Normal forms, melnikov functions and bifurcations of limit cycles, Maoan Han, Pei Yu represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Normal forms, melnikov functions and bifurcations of limit cycles, Maoan Han, Pei Yu represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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
 Language
 eng
 Extent
 1 online resource (xi, 401 pages).
 Contents

 Finding More Limit Cycles Using Melnikov Functions
 Limit Cycle Bifurcations in Equivariant Systems
 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
 Isbn
 9781447129172
 Label
 Normal forms, melnikov functions and bifurcations of limit cycles
 Title
 Normal forms, melnikov functions and bifurcations of limit cycles
 Statement of responsibility
 Maoan Han, Pei Yu
 Subject

 Computer software.
 Differentiable dynamical systems.
 Differential Equations.
 Dynamical Systems and Ergodic Theory.
 Limit cycles
 Limit cycles
 Limit cycles
 MATHEMATICS  Differential Equations  General
 Mathematical Software.
 Mathematics  methods
 Mathematics.
 Nonlinear Dynamics
 Nonlinear Dynamics.
 Nonlinear systems
 Nonlinear systems
 Nonlinear systems
 Ordinary Differential Equations.
 Approximations and Expansions.
 Language
 eng
 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
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorDate
 1961
 http://library.link/vocab/creatorName
 Han, Maoan
 Dewey number
 515/.39
 Index
 index present
 LC call number
 QA371
 LC item number
 .H36 2012
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1947
 http://library.link/vocab/relatedWorkOrContributorName
 Yu, Pei
 Series statement
 Applied mathematical sciences,
 Series volume
 v. 181
 http://library.link/vocab/subjectName

 Limit cycles
 Nonlinear systems
 Mathematics
 Nonlinear Dynamics
 MATHEMATICS
 Limit cycles
 Nonlinear systems
 Label
 Normal forms, melnikov functions and bifurcations of limit cycles, Maoan Han, Pei Yu
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Finding More Limit Cycles Using Melnikov Functions
 Limit Cycle Bifurcations in Equivariant Systems
 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
 Control code
 792942620
 Dimensions
 unknown
 Extent
 1 online resource (xi, 401 pages).
 File format
 unknown
 Form of item
 online
 Isbn
 9781447129172
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)792942620
 Label
 Normal forms, melnikov functions and bifurcations of limit cycles, Maoan Han, Pei Yu
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Finding More Limit Cycles Using Melnikov Functions
 Limit Cycle Bifurcations in Equivariant Systems
 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
 Control code
 792942620
 Dimensions
 unknown
 Extent
 1 online resource (xi, 401 pages).
 File format
 unknown
 Form of item
 online
 Isbn
 9781447129172
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)792942620
Subject
 Computer software.
 Differentiable dynamical systems.
 Differential Equations.
 Dynamical Systems and Ergodic Theory.
 Limit cycles
 Limit cycles
 Limit cycles
 MATHEMATICS  Differential Equations  General
 Mathematical Software.
 Mathematics  methods
 Mathematics.
 Nonlinear Dynamics
 Nonlinear Dynamics.
 Nonlinear systems
 Nonlinear systems
 Nonlinear systems
 Ordinary Differential Equations.
 Approximations and Expansions.
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