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Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience.
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 appli...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton University Press,
2014.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
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| 006 | m o d | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Simiu, Emil. | |
| 245 | 1 | 0 | |a Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : |b Applications of Melnikov Processes in Engineering, Physics, and Neuroscience. |
| 260 | |b Princeton University Press, |c 2014. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |a Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- PART 1. FUNDAMENTALS -- 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 -- PART 2. APPLICATIONS -- 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}2 -- Appendix A5 Elements of Probability Theory -- Appendix A6 Mean Upcrossing Rate ?u-1 for Gaussian Processes -- Appendix A7 Mean Escape Rate ????????-1 for Systems Excited by White Noise -- References -- Index |
| 520 | |a 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. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Differentiable dynamical systems. | |
| 650 | 0 | |a Chaotic behavior in systems. | |
| 650 | 0 | |a Stochastic systems. | |
| 650 | 6 | |a Dynamique différentiable. | |
| 650 | 6 | |a Chaos. | |
| 650 | 6 | |a Systèmes stochastiques. | |
| 650 | 7 | |a MATHEMATICS / Applied. |2 bisacsh | |
| 650 | 7 | |a Chaotic behavior in systems |2 fast | |
| 650 | 7 | |a Differentiable dynamical systems |2 fast | |
| 650 | 7 | |a Stochastic systems |2 fast | |
| 758 | |i has work: |a Chaotic Transitions in Deterministic and Stochastic Dynamical Systems (Online) (Text) |1 https://id.oclc.org/worldcat/entity/E39PCXRgchT7hVXjWqTBG3pRXd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |z 9781322063263 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1756199 |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL1756199 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis28863796 | ||
| 994 | |a 92 |b IZTAP | ||