Multiple-Time-Scale Dynamical Systems

Christopher K.R.T. Jones, Alexander I. Khibnik (Herausgeber)

Buch | Softcover

273 Seiten

2012 | Softcover reprint of the original 1st ed. 2001
Springer-Verlag New York Inc.
978-1-4612-6529-0 (ISBN)

Artikel merken

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.

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.

Reihe/Serie	The IMA Volumes in Mathematics and its Applications ; 122
Zusatzinfo	XI, 273 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	34-02 • 34A26 • 34A34 • 34C20 • 34C215 • 34C23 • 34C26 • 34C29 • 34C37 • 34D15 • 34D35 • 34E10 • 34E15 • 35-01 • 3540 • 35B05 • 35B25 • 35B32 • 35B35 • 92C20
ISBN-10	1-4612-6529-0 / 1461265290
ISBN-13	978-1-4612-6529-0 / 9781461265290
Zustand	Neuware