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Multiple-Time-Scale Dynamical Systems

Name: Multiple-Time-Scale Dynamical Systems
Brand: Springer-Verlag New York Inc.
SKU: 01384268
Price: 160.89 EUR
Availability: InStock
Author: Christopher K. R. T. Jones
ISBN: 9780387951263

Christopher K. R. T. Jones

Alexander I. Khibnik

Lingua

Inglese

Libro Rigido

Codice Libristo: 01384268

Casa editrice Springer-Verlag New York Inc., ottobre 2000

Systems with sub-processes evolving on many different time scales are ubiquitous in applications: ch... Descrizione completa

Codice Libristo: 01384268

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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.