Multiple-Time-Scale Dynamical Systems

Descripción:

Editor(s): Jones, Christopher K.R.T. (Brown University, Providence, RI, USA); Khibnik, Alexander I. (United Technologies Research Center, East Hartford, CT, USA). Series: The IMA Volumes in Mathematics and its Applications. Num Pages: 284 pages, biography. BIC Classification: PBK; PBM; PBP. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 15. Weight in Grams: 444. . 2012. Softcover reprint of the original 1st ed. 2001. Paperback. . . . . Books ship from the US and Ireland. N° de ref. del artículo V9781461265290

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Sinopsis:

Reseña del editor: 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.