Multiple-Time-Scale Dynamical Systems

Alexander I. Khibnik

ISBN 10: 0387951261 / ISBN 13: 9780387951263

Verlag: Springer New York, Springer US Okt 2000, 2000

Beschreibung

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 292 pp. Englisch. Bestandsnummer des Verkäufers 9780387951263

Bibliografische Details

Titel: Multiple-Time-Scale Dynamical Systems

Verlag: Springer New York, Springer US Okt 2000

Erscheinungsdatum: 2000

Einband: Buch

Zustand: Neu

Über diesen Titel

Inhaltsangabe:

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.