Multiple-Time-Scale Dynamical Systems [electronic resource] /

Multiple-Time-Scale Dynamical Systems [electronic resource] /

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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.

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Main Authors: Jones, Christopher K. R. T. editor., Khibnik, Alexander I. editor., SpringerLink (Online service)
Format: Texto biblioteca
Language:eng
Published: New York, NY : Springer New York : Imprint: Springer, 2001
Subjects:Mathematics., Mathematical analysis., Analysis (Mathematics)., Geometry., Topology., Analysis.,
Online Access:http://dx.doi.org/10.1007/978-1-4613-0117-2
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id KOHA-OAI-TEST:185851
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spelling KOHA-OAI-TEST:1858512018-07-30T23:08:25ZMultiple-Time-Scale Dynamical Systems [electronic resource] / Jones, Christopher K. R. T. editor. Khibnik, Alexander I. editor. SpringerLink (Online service) textNew York, NY : Springer New York : Imprint: Springer,2001.engSystems 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.Foreword -- Preface -- Homoclinic orbits to invariant tori in Hamiltonian systems -- Geometric singular perturbation theory beyond normal hyperbolicity -- A primer on the exchange lemma for fast-slow systems -- Geometric analysis of the singularly perturbed planar fold -- Multiple time scales and canards in a chemical oscillator -- A geometric method for periodic orbits in singularly-perturbed systems -- The phenomenon of delayed bifurcation and its analyses -- Synchrony in networks of neuronal oscillators -- Metastable dynamics and exponential asymptotics in multi-dimensional domains -- List of workshop participants.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.Mathematical analysis.Analysis (Mathematics).Geometry.Topology.Mathematics.Analysis.Topology.Geometry.Springer eBookshttp://dx.doi.org/10.1007/978-1-4613-0117-2URN:ISBN:9781461301172
institution COLPOS
collection Koha
country México
countrycode MX
component Bibliográfico
access En linea
En linea
databasecode cat-colpos
tag biblioteca
region America del Norte
libraryname Departamento de documentación y biblioteca de COLPOS
language eng
topic Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Topology.
Mathematics.
Analysis.
Topology.
Geometry.
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Topology.
Mathematics.
Analysis.
Topology.
Geometry.
spellingShingle Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Topology.
Mathematics.
Analysis.
Topology.
Geometry.
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Topology.
Mathematics.
Analysis.
Topology.
Geometry.
Jones, Christopher K. R. T. editor.
Khibnik, Alexander I. editor.
SpringerLink (Online service)
Multiple-Time-Scale Dynamical Systems [electronic resource] /
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.
format Texto
topic_facet Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Geometry.
Topology.
Mathematics.
Analysis.
Topology.
Geometry.
author Jones, Christopher K. R. T. editor.
Khibnik, Alexander I. editor.
SpringerLink (Online service)
author_facet Jones, Christopher K. R. T. editor.
Khibnik, Alexander I. editor.
SpringerLink (Online service)
author_sort Jones, Christopher K. R. T. editor.
title Multiple-Time-Scale Dynamical Systems [electronic resource] /
title_short Multiple-Time-Scale Dynamical Systems [electronic resource] /
title_full Multiple-Time-Scale Dynamical Systems [electronic resource] /
title_fullStr Multiple-Time-Scale Dynamical Systems [electronic resource] /
title_full_unstemmed Multiple-Time-Scale Dynamical Systems [electronic resource] /
title_sort multiple-time-scale dynamical systems [electronic resource] /
publisher New York, NY : Springer New York : Imprint: Springer,
publishDate 2001
url http://dx.doi.org/10.1007/978-1-4613-0117-2
work_keys_str_mv AT joneschristopherkrteditor multipletimescaledynamicalsystemselectronicresource
AT khibnikalexanderieditor multipletimescaledynamicalsystemselectronicresource
AT springerlinkonlineservice multipletimescaledynamicalsystemselectronicresource
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