Senior Research Associate,
School of Mathematics and Statistics, University of Sydney,
Assistant Professor, Department of Mathematics, Colgate University, 2001-2007
Assistant Professor, Department of Mathematics, University of Michigan, 1999-2001
Postdoctoral Member, Institute for Mathematics and its Applications, 1997-1999.
1997-1998 Theme: Emerging Applications of Dynamical Systems
1998-1999 Theme: Mathematics in Biology
Research Assistant, Rensselaer Polytechnic Institute, 1996-1997.
Teaching Assistant, Rensselaer Polytechnic Institute, 1991-1996.
Graduate Research Assistant, Center for Nonlinear Studies,
Los Alamos National Labs, summer, 1994.
Systems Engineer, FACT, Inc., 1986-1991.
Developed several key components of a manufacturing information
management system, including a discrete event simulation for
scheduling work flow in a factory, and a database management
system in a client-server operating system (QNX).
NSF: RUI: Reduced System Computing for Singularly Perturbed
Stabilization of the inverted linearized pendulum
by high frequency vibrations
(with Mark Levi),
SIAM Review, 37(2), 219-223 (1995)
A ball rolling on a freely spinning turntable,
American Journal of Physics, 65(8), (1997)
Numerical computation of canards
(with J. Guckenheimer and K. Hoffman), Int. J. Bif. Chaos, 10, 2669-2687
Global bifurcations of periodic orbits in the forced van der Pol equation
(with J. Guckenheimer and K. Hoffman),
in Global Analysis of Dynamical Systems,
H. W. Broer, B. Krauskopf, G. Vegter, eds.,
Inst. of Physics Publ., Bristol, (2001)
Non-holonomic systems as singular limits for rapid oscillations
(with Mark Levi), Ergodic Theory and Dynamical Systems,22(5), 1497-1506 (2002)
The forced van der Pol equation I: the slow flow and
its bifurcations (with J. Guckenheimer and K. A. Hoffman),
SIAM Journal on Applied Dynamical Systems,2(1), 1-35 (2003)
Resonance in the menstrual cycle: a new model of the LH surge
(with M. L. Zeeman and D. Gokhman),
Reproductive BioMedicine Online,7(3), (2003)
The forced van der Pol equation II: canards in the reduced system
(with K. Bold*, C. Edwards*,
J. Guckenheimer, S. Guharay*,
K. Hoffman, J. Hubbard*, and R. Oliva),
SIAM Journal on Applied Dynamical Systems,2(4) 570-608 (2003)
Canards and horseshoes in the forced van der Pol equation,
Equadiff 2003, Proc. of the Int. Conf. on Diff. Eq., Hasselt, Belgium, F. Dumortier,
H. Broer, J. Mawhin, A. Vanderbauwhede, and S Verduyn Lunel, eds. World Scientific, 2005.
Bifurcations of relaxation oscillations near folded saddles
(with J. Guckenheimer and K. Hoffman), Int. J. Bif. Chaos15(11), (2005).
VFGEN: A Code Generation Tool,
J. Numerical Analysis, Industrial and Applied Math.,
3(1-2) 151-165 (2008).
Bifurcations of mixed-mode oscillations in a stellate cell model
(with Martin Wechselberger), Physica D, 238(16), 1598-1614 (1 August 2009).