Analysis and Simulation of Chaotic Systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2000
|
| Edition: | Second Edition |
| Series: | Applied Mathematical Sciences
94 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable mathematical models that are amenable to further mathematical analysis or to elucidating computer simulations. For the most part, derivations are based on perturbation methods. Because of this, the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. This explains why stability results developed for quite simple problems are often useful for more complicated, even chaotic, ones. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro- differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added |
| Physical Description: | 1 Online-Ressource (XX, 318 p) |
| ISBN: | 9780387226989 9780387989433 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/b98824 |
Staff View
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| spelling | Hoppensteadt, Frank C. Verfasser aut Analysis and Simulation of Chaotic Systems by Frank C. Hoppensteadt Second Edition New York, NY Springer New York 2000 1 Online-Ressource (XX, 318 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 94 0066-5452 Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable mathematical models that are amenable to further mathematical analysis or to elucidating computer simulations. For the most part, derivations are based on perturbation methods. Because of this, the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. This explains why stability results developed for quite simple problems are often useful for more complicated, even chaotic, ones. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro- differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added Mathematics Ecology Global analysis (Mathematics) Biology / Mathematics Analysis Mathematical Biology in General Mathematik Ökologie Chaostheorie (DE-588)4009754-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf 1\p (DE-588)4006432-3 Bibliografie gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Chaotisches System (DE-588)4316104-2 s Dynamisches System (DE-588)4013396-5 s 3\p DE-604 Chaostheorie (DE-588)4009754-7 s 4\p DE-604 https://doi.org/10.1007/b98824 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hoppensteadt, Frank C. Analysis and Simulation of Chaotic Systems Mathematics Ecology Global analysis (Mathematics) Biology / Mathematics Analysis Mathematical Biology in General Mathematik Ökologie Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
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| title | Analysis and Simulation of Chaotic Systems |
| title_auth | Analysis and Simulation of Chaotic Systems |
| title_exact_search | Analysis and Simulation of Chaotic Systems |
| title_full | Analysis and Simulation of Chaotic Systems by Frank C. Hoppensteadt |
| title_fullStr | Analysis and Simulation of Chaotic Systems by Frank C. Hoppensteadt |
| title_full_unstemmed | Analysis and Simulation of Chaotic Systems by Frank C. Hoppensteadt |
| title_short | Analysis and Simulation of Chaotic Systems |
| title_sort | analysis and simulation of chaotic systems |
| topic | Mathematics Ecology Global analysis (Mathematics) Biology / Mathematics Analysis Mathematical Biology in General Mathematik Ökologie Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Mathematics Ecology Global analysis (Mathematics) Biology / Mathematics Analysis Mathematical Biology in General Mathematik Ökologie Chaostheorie Dynamisches System Chaotisches System Bibliografie Lehrbuch |
| url | https://doi.org/10.1007/b98824 |
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