Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

TitleMultiple-Time-Scale Dynamical Systems [electronic resource] / edited by Christopher K. R. T. Jones, Alexander I. Khibnik
ImprintNew York, NY : Springer New York : Imprint: Springer, 2001
Connect tohttp://dx.doi.org/10.1007/978-1-4613-0117-2
Descript XI, 273 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Mathematical analysis Analysis (Mathematics) Geometry Topology Mathematics Analysis Topology Geometry



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram