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Multiple-Time-Scale Dynamical Systems

  • Christopher K. R. T. Jones
  • Alexander I. Khibnik

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Amadeu Delshams, Pere Gutiérrez
    Pages 1-27
  3. Freddy Dumortier, Robert Roussarie
    Pages 29-63
  4. Tasso J. Kaper, Christopher K. R. T. Jones
    Pages 65-87
  5. Alexandra Milik, Peter Szmolyan
    Pages 117-140
  6. Back Matter
    Pages 261-273

About these proceedings

Introduction

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.

Keywords

Volume bifurcation dynamical systems dynamics hamiltonian system

Editors and affiliations

  • Christopher K. R. T. Jones
    • 1
  • Alexander I. Khibnik
    • 2
  1. 1.Division of Applied Mathematics and Lefschetz Center for Dynamical SystemsBrown UniversityProvidenceUSA
  2. 2.United Technologies Research CenterEast HartfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0117-2
  • Copyright Information Springer-Verlag New York, Inc. 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6529-0
  • Online ISBN 978-1-4613-0117-2
  • Series Print ISSN 0940-6573
  • Buy this book on publisher's site