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Multiple-Time-Scale Dynamical Systems

  • Conference proceedings
  • © 2001

Overview

Editors:
  1. Christopher K. R. T. Jones

    1. Division of Applied Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Providence, USA

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  2. Alexander I. Khibnik

    1. United Technologies Research Center, East Hartford, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 122)

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Table of contents (9 papers)

  1. Front Matter

    Pages i-xi
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  2. Homoclinic Orbits to Invariant Tori in Hamiltonian Systems

    • Amadeu Delshams, Pere Gutiérrez
    Pages 1-27

  3. Geometric Singular Perturbation Theory Beyond Normal Hyperbolicity

    • Freddy Dumortier, Robert Roussarie
    Pages 29-63

  4. A Primer on the Exchange Lemma for Fast-Slow Systems

    • Tasso J. Kaper, Christopher K. R. T. Jones
    Pages 65-87

  5. Geometric Analysis of the Singularly Perturbed Planar Fold

    • M. Krupa, P. Szmolyan
    Pages 89-116

  6. Multiple Time Scales and Canards in a Chemical Oscillator

    • Alexandra Milik, Peter Szmolyan
    Pages 117-140

  7. A Geometric Method for Periodic Orbits in Singularly-Perturbed Systems

    • Cristina Soto-Treviño
    Pages 141-202

  8. The Phenomenon of Delayed Bifurcation and its Analyses

    • Jianzhong Su
    Pages 203-214

  9. Synchrony in Networks of Neuronal Oscillators

    • D. Terman
    Pages 215-232

  10. Metastable dynamics and exponential asymptotics in multi-dimensional domains

    • Michael J. Ward
    Pages 233-259

  11. Back Matter

    Pages 261-273
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Keywords

About this book

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.

Editors and Affiliations

  • Division of Applied Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Providence, USA

    Christopher K. R. T. Jones

  • United Technologies Research Center, East Hartford, USA

    Alexander I. Khibnik

Bibliographic Information

  • Book Title: Multiple-Time-Scale Dynamical Systems

  • Editors: Christopher K. R. T. Jones, Alexander I. Khibnik

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4613-0117-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 2001

  • Hardcover ISBN: 978-0-387-95126-3Published: 06 October 2000

  • Softcover ISBN: 978-1-4612-6529-0Published: 13 September 2012

  • eBook ISBN: 978-1-4613-0117-2Published: 06 December 2012

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: XI, 273

  • Topics: Analysis, Topology, Geometry

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