HOME    »    PROGRAMS/ACTIVITIES    »    Annual Thematic Program
Multiple-Time-Scale Dynamical Systems
October 27 - 31, 1997


Fred Dumortier, Limburgs Universitair Centrum
Chris Jones, Brown University (Chair)
Alexander Khibnik, Cornell University
David Terman, Ohio State
Steve Wiggins, Caltech

Many physical problems, particularly in chemical and biological systems, involve processes that occur on widely varying time scales. The resulting model is a system that has a singular perturbation character. Such problems have motivated the development of much mathematical theory, including classical asymptotic theory and a geometric theory based on invariant manifolds. The phenomena that appear in singular-perturbation problems are subtle, often involving expansions in terms of quantities that are exponentially small in terms of a small parameter in the problem. The singular structure of these equations can also pose formidable numerical challenges. The goal of this workshop was to explore the connection between the asymptotic and geometric theories, with a particular emphasis on exponentially small phenomena, and to bring researchers developing these methods together with people working on applications in biology, chemistry and mechanics.

Click on the titles to find abstracts and/or links to presentation materials

W. Miller, R. Gulliver,
C. Jones
Welcome and Orientation
David McLaughlin,
Courant Institute, NYU
Chaotic and Homoclinic Behavior in PDE's
Nigel Goldenfeld,
University of Illinois
Renormalization Group Approach to Global Asymptotic Analysis
Amadeu Delshams,
Univ. Politécnica de Catalunya
Homoclinic orbits to invariant tori in Hamiltonian Systems
Richard Haberman,
Southern Methodist Univ.
Slow passage through a homoclinic orbit with subharmonic resonances
Alexandra Milik,
Techn. Univ. of Vienna
The Geometry of Mixed-mode Oscillations in a Chemical Oscillator
Konstantin Mischaikow,
Georgia Institute of Technology
A topological approach to fast-slow dynamics
Michael J. Davis,
Argonne National Laboratory
Some Multiple-Time-Scale Problems in Chemical Dynamics, Molecular Spectroscopy, & Kinetic Modeling
Linda Petzold,
University of California-Santa Barbara
Model Reduction for Nonlinear Dynamical Systems from Chemical Kinetics
Michael Ward,
University of British Columbia
Dynamic Metastability for Reaction-Diffusion Equations
Xiao-Biao Lin,
North Carolina State University
Method of singular characteristics for Hamilton-Jacobi equations that develop shock structures
Mohammed Ziane,
Stanford University
A mathematical formulation of the Goldenfeld renormalization group method
Jiangzhong Su,
Univ. of Texas at Arlington
Delay of bifurcation phenomena and their analysis
Anatoly Neishtadt,
Space Research Institute, Moscow
On stability loss delay f or dynamical bifurcations
Robert A. Gardner,
University of Massachusetts
Stability Analysis of Singular Patterns for the 1-D Gray-Scott Model
David Terman,
Ohio State University
Multiple Time Scales in Networks of Neural Oscillators
Tasso Kaper,
Boston University
Exchange lemmas: an overveiew and some new applications
Chongchun Zeng,
Courant Institute, NYU
Invariant Manifolds and Invariant Foliations for Semiflows in Banach Space
Yulij Ilyashenko,
Cornell University/ Moscow State & Indep. Universities
Embedding theorems for maps and normal forms for the slow-fast systems
George Haller,
Brown University
Homoclinic jumping in evolution equations
Robert Roussarie,
University of Bourgogne
Multiple Canard Cycles in Van Der Pol-like Equations
Pavol Brunovsky,
Cornenius University
Ck inclination theorems for singularly perturbed problems
Peter Szmolyan,
Technische Universität Wein
Extending Geometric Singular Perturbation Theory to Non-hyperbolic Points
Discussion Session Panel: Marc Diener, Freddy Dumortier, Paul Fife, Chris Jones, David McLaughlin
Petar Kokotovic,
University of California-Santa Barbara
Singular Perturbations and Multiple Time Scales in Control System Modeling and Design
Dennis Perchak,
This talk is joint with the IMA Seminar on Industrial Problems:

Stokesian Dynamics Simulation of Interacting Solid Particles

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1997-1998 Emerging Applications of Dynamical Systems