Multiple-Time-Scale Dynamical Systems

. Ed(s): Jones, Christopher K.R.T. (Brown University, Providence, RI, USA); Khibnik, Alexander I. (United Technologies Research Center, East Hartford

ISBN 10: 1461265290 / ISBN 13: 9781461265290

Editore: Springer-Verlag New York Inc., 2012

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. Codice articolo V9781461265290

Riassunto:

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.

Contenuti: Foreword.- Preface.- Homoclinic orbits to invariant tori in Hamiltonian systems.- Geometric singular perturbation theory beyond normal hyperbolicity.- A primer on the exchange lemma for fast-slow systems.- Geometric analysis of the singularly perturbed planar fold.- Multiple time scales and canards in a chemical oscillator.- A geometric method for periodic orbits in singularly-perturbed systems.- The phenomenon of delayed bifurcation and its analyses.- Synchrony in networks of neuronal oscillators.- Metastable dynamics and exponential asymptotics in multi-dimensional domains.- List of workshop participants.

Dati bibliografici

Titolo: Multiple-Time-Scale Dynamical Systems
Casa editrice: Springer-Verlag New York Inc.
Data di pubblicazione: 2012
Legatura: Brossura
Condizione: New