The Resource Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience, Emil Simiu
Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience, Emil Simiu
Resource Information
The item Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience, Emil Simiu represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience, Emil Simiu represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.
This item is available to borrow from 1 library branch.
 Summary
 The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, statedependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a firstyear graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology
 Language
 eng
 Extent
 1 online resource (241 pages)
 Contents

 Frontmatter
 Contents
 Preface
 Chapter 1. Introduction
 Chapter 2. Transitions in Deterministic Systems and the Melnikov Function
 Chapter 3. Chaos in Deterministic Systems and the Melnikov Function
 Chapter 4. Stochastic Processes
 Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process
 Chapter 6. Vessel Capsizing
 Chapter 7. OpenLoop Control of Escapes in Stochastically Excited Systems
 Chapter 8. Stochastic Resonance
 Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a FirstOrder Dynamical System
 Chapter 10. SnapThrough of Transversely Excited Buckled Column
 Chapter 11. WindInduced AlongShore Currents over a Corrugated Ocean Floor
 Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System
 Appendix A1 Derivation of Expression for the Melnikov Function
 Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds
 Appendix A3 Topological Conjugacy
 Appendix A4 Properties of Space {u2211}
 Appendix A5 Elements of Probability Theory
 Appendix A6 Mean Upcrossing Rate x
 Appendix A7 Mean Escape Rate x
 References
 Index
 Isbn
 9780691144344
 Label
 Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience
 Title
 Chaotic transitions in deterministic and stochastic dynamical systems
 Title remainder
 applications of Melnikov processes in engineering, physics, and neuroscience
 Statement of responsibility
 Emil Simiu
 Subject

 Chaotic behavior in systems
 Differentiable dynamical systems
 Differentiable dynamical systems
 Electronic books
 MATHEMATICS  Applied
 MATHEMATICS  Calculus
 MATHEMATICS  Mathematical Analysis
 Mathematics
 Mathematik
 Stochastic systems
 Stochastic systems
 Applied Mathematics
 Chaotic behavior in systems
 Language
 eng
 Summary
 The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, statedependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a firstyear graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology
 Cataloging source
 E7B
 http://library.link/vocab/creatorName
 Simiu, Emil
 Dewey number
 515/.352
 Illustrations
 illustrations
 Index
 index present
 Language note
 In English
 LC call number
 QA614.8
 LC item number
 .S55 2002eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Princeton Series in Applied Mathematics
 http://library.link/vocab/subjectName

 Differentiable dynamical systems
 Chaotic behavior in systems
 Stochastic systems
 MATHEMATICS
 MATHEMATICS
 MATHEMATICS
 Chaotic behavior in systems
 Differentiable dynamical systems
 Stochastic systems
 Applied Mathematics
 Chaotic behavior in systems
 Differentiable dynamical systems
 Mathematics
 Stochastic systems
 Mathematik
 Label
 Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience, Emil Simiu
 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
 Frontmatter  Contents  Preface  Chapter 1. Introduction  Chapter 2. Transitions in Deterministic Systems and the Melnikov Function  Chapter 3. Chaos in Deterministic Systems and the Melnikov Function  Chapter 4. Stochastic Processes  Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process  Chapter 6. Vessel Capsizing  Chapter 7. OpenLoop Control of Escapes in Stochastically Excited Systems  Chapter 8. Stochastic Resonance  Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a FirstOrder Dynamical System  Chapter 10. SnapThrough of Transversely Excited Buckled Column  Chapter 11. WindInduced AlongShore Currents over a Corrugated Ocean Floor  Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System  Appendix A1 Derivation of Expression for the Melnikov Function  Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds  Appendix A3 Topological Conjugacy  Appendix A4 Properties of Space {u2211}  Appendix A5 Elements of Probability Theory  Appendix A6 Mean Upcrossing Rate x  Appendix A7 Mean Escape Rate x  References  Index
 Control code
 891400514
 Dimensions
 unknown
 Extent
 1 online resource (241 pages)
 Form of item
 online
 Isbn
 9780691144344
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1515/9781400832507
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 22573/ctt767zdv
 Specific material designation
 remote
 System control number
 (OCoLC)891400514
 Label
 Chaotic transitions in deterministic and stochastic dynamical systems : applications of Melnikov processes in engineering, physics, and neuroscience, Emil Simiu
 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
 Frontmatter  Contents  Preface  Chapter 1. Introduction  Chapter 2. Transitions in Deterministic Systems and the Melnikov Function  Chapter 3. Chaos in Deterministic Systems and the Melnikov Function  Chapter 4. Stochastic Processes  Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process  Chapter 6. Vessel Capsizing  Chapter 7. OpenLoop Control of Escapes in Stochastically Excited Systems  Chapter 8. Stochastic Resonance  Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a FirstOrder Dynamical System  Chapter 10. SnapThrough of Transversely Excited Buckled Column  Chapter 11. WindInduced AlongShore Currents over a Corrugated Ocean Floor  Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System  Appendix A1 Derivation of Expression for the Melnikov Function  Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds  Appendix A3 Topological Conjugacy  Appendix A4 Properties of Space {u2211}  Appendix A5 Elements of Probability Theory  Appendix A6 Mean Upcrossing Rate x  Appendix A7 Mean Escape Rate x  References  Index
 Control code
 891400514
 Dimensions
 unknown
 Extent
 1 online resource (241 pages)
 Form of item
 online
 Isbn
 9780691144344
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1515/9781400832507
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 22573/ctt767zdv
 Specific material designation
 remote
 System control number
 (OCoLC)891400514
Subject
 Chaotic behavior in systems
 Differentiable dynamical systems
 Differentiable dynamical systems
 Electronic books
 MATHEMATICS  Applied
 MATHEMATICS  Calculus
 MATHEMATICS  Mathematical Analysis
 Mathematics
 Mathematik
 Stochastic systems
 Stochastic systems
 Applied Mathematics
 Chaotic behavior in systems
Genre
Member of
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