Speaker: Prof. John M. Guckenheimer, Mathematics Department, Cornell University, Ithaca, New York
URL for Speaker: http://www.math.cornell.edu/~gucken/
Location: LSK 301
Biological and chemical systems display bursting and mixed mode oscillations. This lecture will survey recent advances in the theory of dynamical systems with multiple time scales that has dramatically improved our understanding of these complex temporal behaviors. A natural classification of different types of bursting and mixed modes is developed and used as a foundation for numerical methods that analyze multiple time scale models. These methods are applied to mixed mode oscillations of chemical reactions that were intensively studied thirty years ago without producing models that faithfully reproduced experimental observations. Additional examples are drawn from neuroscience.
John Guckenheimer obtained his Ph.D. from University of California at Berkeley in 1970 and is currently the Abram R. Bullis Professor in Mathematics at Cornell University. His research is a blend of theoretical investigation, development of computer methods and studies of nonlinear systems that arise in diverse fields of science and engineering. Two of the primary themes have been bifurcation theory and the effects of multiple time scales in shaping dynamical behavior. Application areas in which he has worked include population biology, fluid dynamics, neurosciences, animal locomotion and control of nonlinear systems. His work on algorithm development includes contributions to methods for computing bifurcations, periodic orbits and invariant manifolds of vector fields and for the analysis of fractal dimensions of attractors.