The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1982
|
| Schriftenreihe: | Applied Mathematical Sciences
41 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense |
| Beschreibung: | 1 Online-Ressource (XII, 273p. 91 illus) |
| ISBN: | 9781461257677 9780387907758 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4612-5767-7 |
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| 500 | |a The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Sparrow, Colin |
| author_facet | Sparrow, Colin |
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| doi_str_mv | 10.1007/978-1-4612-5767-7 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461257677 9780387907758 |
| issn | 0066-5452 |
| language | English |
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| spelling | Sparrow, Colin aut The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors by Colin Sparrow New York, NY Springer New York 1982 1 Online-Ressource (XII, 273p. 91 illus) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 41 0066-5452 The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense Physics Thermodynamics Statistical Physics, Dynamical Systems and Complexity Lorenz-Gleichung (DE-588)4776099-0 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Seltsamer Attraktor (DE-588)4140566-3 gnd rswk-swf Lorenz-Gleichung (DE-588)4776099-0 s Verzweigung Mathematik (DE-588)4078889-1 s 1\p DE-604 Seltsamer Attraktor (DE-588)4140566-3 s 2\p DE-604 Erscheint auch als Druck-Ausgabe 978-0-387-90775-8 https://doi.org/10.1007/978-1-4612-5767-7 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 |
| spellingShingle | Sparrow, Colin The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors Physics Thermodynamics Statistical Physics, Dynamical Systems and Complexity Lorenz-Gleichung (DE-588)4776099-0 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Seltsamer Attraktor (DE-588)4140566-3 gnd |
| subject_GND | (DE-588)4776099-0 (DE-588)4078889-1 (DE-588)4140566-3 |
| title | The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors |
| title_auth | The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors |
| title_exact_search | The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors |
| title_full | The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors by Colin Sparrow |
| title_fullStr | The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors by Colin Sparrow |
| title_full_unstemmed | The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors by Colin Sparrow |
| title_short | The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors |
| title_sort | the lorenz equations bifurcations chaos and strange attractors |
| topic | Physics Thermodynamics Statistical Physics, Dynamical Systems and Complexity Lorenz-Gleichung (DE-588)4776099-0 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Seltsamer Attraktor (DE-588)4140566-3 gnd |
| topic_facet | Physics Thermodynamics Statistical Physics, Dynamical Systems and Complexity Lorenz-Gleichung Verzweigung Mathematik Seltsamer Attraktor |
| url | https://doi.org/10.1007/978-1-4612-5767-7 |
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