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Hunting ducks and nondeterminism in nonsmooth dynamics
Friday, February 12, 2010 - 3:15pm

Portland State University
Fariborz Maseeh Department of Mathematics & Statistics

The Maseeh Mathematics and Statistics Colloquium Series*
presents

Mike Jeffrey, Ph.D.
~ Applied Nonlinear Mathematics Group,
University of Bristol ~

Hunting ducks and nondeterminism in nonsmooth dynamics
Abstract:
The effectiveness of physical theories depends heavily upon context -- the parameter regime in which a particular theory/model makes a problem solvable. The real world of nature and engineering, however, consists of multiple systems, all with different structures and different scales, and therefore different models. Bring two different systems into contact and the results are often highly nonsmooth -- e.g. impact, friction, and bursting -- and are still barely understood. The theory of nonsmooth dynamical systems is young, but fruitful. A nonsmooth jump in phase space is something much more violent than familiar sudden events, like bifurcations. Particular interest lies in trajectories that stick to and slide along discontinuity surfaces in phase space (Filippov systems). These cause 'sliding bifurcations', which we recently showed can destroy stable and periodic dynamics without warning. As we will discuss: these were recently observed in a superconducting sensor, they pose problems for our understanding of fundamental mechanics and control by giving rise to nondeterministic chaos, and they offer new insight into the "Canard" (french duck) phenomenon. Canards are related to relaxation oscillations and the neuronal spiking responsible for epilepsy, and having taken a journey through the nonsmooth world we are led back, via a relation with ''non-standard analysis'', towards an understanding of what puts the ''non'' into ''nonsmooth''.

Friday, February 12, 2010, 3:15pm
Neuberger Hall Room 381
(Refreshments served at 3:00 in Neuberger Hall room 344)

* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU. This event is free and open to the public.


Contact Person:
Kathie Leck
Office Staff
Fariborz Maseeh Department of
Mathematics & Statistics
Portland State University
Phone: 503-725-8244, Fax: 503-725-3661