Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Applications of Melnikov Processes in Engineering, Physics, and Neuroscience
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2002]
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| Schriftenreihe: | Princeton Series in Applied Mathematics
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (240p.) |
| ISBN: | 9781400832507 |
| DOI: | 10.1515/9781400832507 |
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| 500 | |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 | ||
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| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400832507 |
| format | Electronic eBook |
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| id | DE-604.BV042522601 |
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| indexdate | 2024-07-10T01:24:01Z |
| institution | BVB |
| isbn | 9781400832507 |
| language | English |
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| publisher | Princeton University Press |
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| spelling | Simiu, Emil Verfasser aut Chaotic Transitions in Deterministic and Stochastic Dynamical Systems Applications of Melnikov Processes in Engineering, Physics, and Neuroscience Emil Simiu Princeton, N.J. Princeton University Press [2002] 1 Online-Ressource (240p.) txt rdacontent c rdamedia cr rdacarrier Princeton Series in Applied Mathematics 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 In English Mathematik Differentiable dynamical systems Chaotic behavior in systems Stochastic systems MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh MATHEMATICS / Applied bisacsh Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Stochastisches dynamisches System (DE-588)4305316-6 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Stochastisches dynamisches System (DE-588)4305316-6 s Chaotisches System (DE-588)4316104-2 s 1\p DE-604 https://doi.org/10.1515/9781400832507 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Simiu, Emil Chaotic Transitions in Deterministic and Stochastic Dynamical Systems Applications of Melnikov Processes in Engineering, Physics, and Neuroscience Mathematik Differentiable dynamical systems Chaotic behavior in systems Stochastic systems MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh MATHEMATICS / Applied bisacsh Differenzierbares dynamisches System (DE-588)4137931-7 gnd Stochastisches dynamisches System (DE-588)4305316-6 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4305316-6 (DE-588)4316104-2 |
| title | Chaotic Transitions in Deterministic and Stochastic Dynamical Systems Applications of Melnikov Processes in Engineering, Physics, and Neuroscience |
| title_auth | Chaotic Transitions in Deterministic and Stochastic Dynamical Systems Applications of Melnikov Processes in Engineering, Physics, and Neuroscience |
| title_exact_search | Chaotic Transitions in Deterministic and Stochastic Dynamical Systems Applications of Melnikov Processes in Engineering, Physics, and Neuroscience |
| title_full | Chaotic Transitions in Deterministic and Stochastic Dynamical Systems Applications of Melnikov Processes in Engineering, Physics, and Neuroscience Emil Simiu |
| title_fullStr | Chaotic Transitions in Deterministic and Stochastic Dynamical Systems Applications of Melnikov Processes in Engineering, Physics, and Neuroscience Emil Simiu |
| title_full_unstemmed | Chaotic Transitions in Deterministic and Stochastic Dynamical Systems Applications of Melnikov Processes in Engineering, Physics, and Neuroscience Emil Simiu |
| title_short | Chaotic Transitions in Deterministic and Stochastic Dynamical Systems |
| title_sort | chaotic transitions in deterministic and stochastic dynamical systems applications of melnikov processes in engineering physics and neuroscience |
| title_sub | Applications of Melnikov Processes in Engineering, Physics, and Neuroscience |
| topic | Mathematik Differentiable dynamical systems Chaotic behavior in systems Stochastic systems MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh MATHEMATICS / Applied bisacsh Differenzierbares dynamisches System (DE-588)4137931-7 gnd Stochastisches dynamisches System (DE-588)4305316-6 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Mathematik Differentiable dynamical systems Chaotic behavior in systems Stochastic systems MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis MATHEMATICS / Applied Differenzierbares dynamisches System Stochastisches dynamisches System Chaotisches System |
| url | https://doi.org/10.1515/9781400832507 |
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