Multiple-Time-Scale Dynamical Systems (Hardcover)

Christopher K.R.T. Jones

ISBN 10: 0387951261 / ISBN 13: 9780387951263

Editore: Springer-Verlag New York Inc., New York, NY, 2000

Riguardo questo articolo

Hardcover. 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. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9780387951263

Dati bibliografici

• Titolo: Multiple-Time-Scale Dynamical Systems (Hardcover)
• Editore: Springer-Verlag New York Inc., New York, NY
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 0387951261
• ISBN 13: 9780387951263
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

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.