IAM-PIMS-MITACS Distinguished Colloquium: John Guckenheimer

Abstract:

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.