TY - BOOK UR - http://lib.ugent.be/catalog/ebk01:3710000000222321 ID - ebk01:3710000000222321 LA - eng TI - Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : Applications of Melnikov Processes in Engineering, Physics, and Neuroscience PY - 2002 SN - 9781400832507 AU - Simiu, Emil, author. AB - 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. ER -Download RIS file
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020 | a 9781400832507 | ||
024 | 7 | a 10.1515/9781400832507 2 doi | |
035 | a (DE-B1597)447398 | ||
035 | a (OCoLC)891400514 | ||
040 | a IN-ChSCO b eng c IN-ChSCO e rda | ||
041 | a eng | ||
050 | 4 | a QA614.8 | |
050 | 1 | 4 | a QA614.8 b .S55 2002eb |
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072 | 7 | a MAT003000 2 bisacsh | |
082 | 4 | a 515/.352 2 21 | |
082 | 4 | a 515/.352 2 23 | |
100 | 1 | a Simiu, Emil, e author. | |
245 | 1 | a Chaotic Transitions in Deterministic and Stochastic Dynamical Systems : b Applications of Melnikov Processes in Engineering, Physics, and Neuroscience / c Emil Simiu. | |
264 | 1 | a Princeton, N.J. : b Princeton University Press, c [2002] | |
264 | 4 | c ©2002 | |
300 | a 1 online resource(240p.) : b illustrations. | ||
336 | a text 2 rdacontent | ||
337 | a computer 2 rdamedia | ||
338 | a online resource 2 rdacarrier | ||
347 | a text file b PDF 2 rda | ||
490 | a Princeton Series in Applied Mathematics | ||
505 | t Frontmatter -- t Contents -- t Preface -- t Chapter 1. Introduction -- t Chapter 2. Transitions in Deterministic Systems and the Melnikov Function -- t Chapter 3. Chaos in Deterministic Systems and the Melnikov Function -- t Chapter 4. Stochastic Processes -- t Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process -- t Chapter 6. Vessel Capsizing -- t Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems -- t Chapter 8. Stochastic Resonance -- t Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System -- t Chapter 10. Snap-Through of Transversely Excited Buckled Column -- t Chapter 11. Wind-Induced Along-Shore Currents over a Corrugated Ocean Floor -- t Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System -- t Appendix A1 Derivation of Expression for the Melnikov Function -- t Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds -- t Appendix A3 Topological Conjugacy -- t Appendix A4 Properties of Space ∑ -- t Appendix A5 Elements of Probability Theory -- t Appendix A6 Mean Upcrossing Rate τ -- t Appendix A7 Mean Escape Rate τ -- t References -- t 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. | ||
533 | a Electronic reproduction. b Princeton, N.J. : c Princeton University Press, d 2002. n Mode of access: World Wide Web. n System requirements: Web browser. n Access may be restricted to users at subscribing institutions. | ||
538 | a Mode of access: Internet via World Wide Web. | ||
545 | a SimiuEmil: Emil Simiu is a NIST Fellow, National Institute of Standards and Technology, and Research Professor, Whiting School of Engineering, The Johns Hopkins University. A specialist in flow-structure interaction, he is the coauthor of "Wind Effects on Structures" and was the 1984 recipient of the Federal Engineer of the Year award. | ||
546 | a In English. | ||
588 | a Description based on online resource; title from PDF title page (publisher’s Web site, viewed March 24, 2015) | ||
650 | a Chaotic behavior in systems. | ||
650 | a Differentiable dynamical systems. | ||
650 | a Stochastic systems. | ||
650 | 4 | a Applied Mathematics. | |
650 | 4 | a Chaotic behavior in systems. | |
650 | 4 | a Differentiable dynamical systems. | |
650 | 4 | a Mathematics. | |
650 | 4 | a Stochastic systems. | |
650 | 7 | a MATHEMATICS x Applied. 2 bisacsh. | |
650 | 7 | a MATHEMATICS x Calculus. 2 bisacsh. | |
650 | 7 | a MATHEMATICS x Mathematical Analysis. 2 bisacsh. | |
650 | 7 | a Mathematik. | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2013 z 978-3-11-044250-2 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2014 z 978-3-11-045953-1 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Series in Applied Mathematics ebook package z 978-3-11-051583-1 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Univ. Press eBook Package 2014 z 978-3-11-041342-7 | |
856 | 4 | u https://doi.org/10.1515/9781400832507 | |
856 | 4 | 2 | 3 Cover u https://www.degruyter.com/doc/cover/9781400832507.jpg |
912 | a 978-3-11-041342-7 Princeton Univ. Press eBook Package 2014 | ||
912 | a 978-3-11-044250-2 Princeton eBook Package Backlist 2000-2013 | ||
912 | a 978-3-11-045953-1 Princeton eBook Package Backlist 2000-2014 | ||
912 | a 978-3-11-051583-1 Princeton Series in Applied Mathematics ebook package | ||
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