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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

Creator
Author
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, state-dependent, 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 first-year 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
Work
Publication
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. Open-Loop Control of Escapes in Stochastically Excited Systems
  • Chapter 8. Stochastic Resonance
  • Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System
  • Chapter 10. Snap-Through of Transversely Excited Buckled Column
  • Chapter 11. Wind-Induced Along-Shore 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
Instance
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
Creator
Author
Subject
Genre
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, state-dependent, 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 first-year 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
Member of
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
Instantiates
Publication
Copyright
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. Open-Loop Control of Escapes in Stochastically Excited Systems -- Chapter 8. Stochastic Resonance -- Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- Chapter 10. Snap-Through of Transversely Excited Buckled Column -- Chapter 11. Wind-Induced Along-Shore 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
Publication
Copyright
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. Open-Loop Control of Escapes in Stochastically Excited Systems -- Chapter 8. Stochastic Resonance -- Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- Chapter 10. Snap-Through of Transversely Excited Buckled Column -- Chapter 11. Wind-Induced Along-Shore 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

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