Multiple-Time-Scale Dynamical Systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2001
|
| Series: | The IMA Volumes in Mathematics and its Applications
122 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators |
| Physical Description: | 1 Online-Ressource (XI, 273 p) |
| ISBN: | 9781461301172 9781461265290 |
| ISSN: | 0940-6573 |
| DOI: | 10.1007/978-1-4613-0117-2 |
Staff View
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| spelling | Jones, Christopher K. R. T. Verfasser aut Multiple-Time-Scale Dynamical Systems edited by Christopher K. R. T. Jones, Alexander I. Khibnik New York, NY Springer New York 2001 1 Online-Ressource (XI, 273 p) txt rdacontent c rdamedia cr rdacarrier The IMA Volumes in Mathematics and its Applications 122 0940-6573 Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators Mathematics Global analysis (Mathematics) Geometry Topology Analysis Mathematik Differentialgleichungssystem (DE-588)4121137-6 gnd rswk-swf Singuläre Störung (DE-588)4055100-3 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1997 Minneapolis Minn. gnd-content Differentialgleichungssystem (DE-588)4121137-6 s Singuläre Störung (DE-588)4055100-3 s 2\p DE-604 Khibnik, Alexander I. Sonstige oth https://doi.org/10.1007/978-1-4613-0117-2 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 | Jones, Christopher K. R. T. Multiple-Time-Scale Dynamical Systems Mathematics Global analysis (Mathematics) Geometry Topology Analysis Mathematik Differentialgleichungssystem (DE-588)4121137-6 gnd Singuläre Störung (DE-588)4055100-3 gnd |
| subject_GND | (DE-588)4121137-6 (DE-588)4055100-3 (DE-588)1071861417 |
| title | Multiple-Time-Scale Dynamical Systems |
| title_auth | Multiple-Time-Scale Dynamical Systems |
| title_exact_search | Multiple-Time-Scale Dynamical Systems |
| title_full | Multiple-Time-Scale Dynamical Systems edited by Christopher K. R. T. Jones, Alexander I. Khibnik |
| title_fullStr | Multiple-Time-Scale Dynamical Systems edited by Christopher K. R. T. Jones, Alexander I. Khibnik |
| title_full_unstemmed | Multiple-Time-Scale Dynamical Systems edited by Christopher K. R. T. Jones, Alexander I. Khibnik |
| title_short | Multiple-Time-Scale Dynamical Systems |
| title_sort | multiple time scale dynamical systems |
| topic | Mathematics Global analysis (Mathematics) Geometry Topology Analysis Mathematik Differentialgleichungssystem (DE-588)4121137-6 gnd Singuläre Störung (DE-588)4055100-3 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Geometry Topology Analysis Mathematik Differentialgleichungssystem Singuläre Störung Konferenzschrift 1997 Minneapolis Minn. |
| url | https://doi.org/10.1007/978-1-4613-0117-2 |
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