ENGLISH

Multiple-Time-Scale Dynamical Systems

By Amadeu Delshams , Pere Gutiérrez (auth.) , Christopher K. R. T. Jones , Alexander I. Khibnik (eds.)

Book information

Publisher
Springer-Verlag New York
Year
2001
ISBN
978-1-4612-6529-0, 978-1-4613-0117-2
DOI
10.1007/978-1-4613-0117-2
Language
english
Format
PDF
Filesize
7 MB (7439484 bytes)
Series
The IMA Volumes in Mathematics and its Applications 122
Edition
1
Pages
273\277
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Analysis; Topology; Geometry

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.

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