Sue Ann Campbell
Research
My research involves building and analyzing mathematical models for a variety
of biological and physical systems. Particular applications I have studied
include metal cutting, biological and artificial neural networks and feedback
control systems. Although physically unrelated, the behaviour of the these
systems is influenced by the same factors: the presence of nonlinearities and
time delays. The time delays represent the time it takes information to
propagate from one part of the system to another. The nonlinearity represents
the fact that in these systems a small change in the state can often result in
a large change in behaviour. Mathematically, my research involves
dynamical systems theory (e.g., stability, bifurcations, centre manifolds and
normal forms) and its extensions to delay differential equations.
A detailed description of my current research projects is also available.
- Publications
- Graduate Students
- Laila Alsharief (Ph.D., current) - Time delays and models for balance
control.
- Drew Lloyd (M.Math, current) - Modelling the electrical activity of
Aplysia
bag cell neurons.
- Raluca Jessop (Ph.D., current) - Dynamics of neural systems with
distributed delays. Papers: 1
- Katie Ferguson (M.Math, August 2009) - Modelling CA1 hippocampal neurons and
astrocyte interactions. Poster
- Ilya Kobelevskiy (M.Math, August 2008) - Type I neural oscillators with
time delayed connections.
- Andrew Smith (M.Math, June 2007) - Phase models for Fitzhugh-Nagumo
oscillators with time delayed connections.
- Hojjat Bazzazi (M.Math, August 2005) - Synchronization in hippocampal
neural models.
Paper
- Sehjeong Kim (Ph.D., August 2005) - Switching systems with delayed feedback control.
Papers: 1
2
-
Richard Taylor (Ph.D., May 2004) - Probabilistic properties of delay
differential equations. Paper
- Israel Ncube (Ph.D., May 2001) - Stochastic approximation of
artificial neural network-type learning algorithms: a dynamical
systems approach. Papers: 1
2
- Leslie Shayer (M.Math., August 1998) - Analysis of a system
of two coupled neurons with two time delays.
Paper
- Postdoctoral Researchers
- Sharene Bungay - Numerical bifurcation analysis of rings of neurons
with time delayed connections. (January 2004 - August 2005).
Papers: 1
2. Animations
- Israel Ncube - Symmetric Hopf bifurcation in neural systems
(July-August 2002). Paper.
- Yuan Yuan
- Rings of neurons with delayed conections.
(July-August 2002). Papers: 1
2.
- Huaiping Zhu -
Predator-prey systems/neural networks (September
1999-August 2000). Paper.
- Undergraduate Researchers
- Software I use in my research
- XPPAUT (numerical integration of delay differential equations,
among other things)
- AUTO (bifurcation
continuation for ODE's)
-
DDE-BIFTOOL (bifurcation continutation for delay differential equations)
- MATCONT (bifurcation
continuation software for ODE's that runs under Matlab.)
- Research Affiliations
- Journal Affiliations
Teaching
- Fall 2009
- AMATH 350 - Differential Equations for Business and Economics
- Winter 2009
-
Mathematical Associations to which I belong
Other Interests and Affiliations
Some mathematically related links
How to reach me
office: MC5124
phone: (519) 888-4567 Ext. 35461
fax: (519) 746-4319
email:
sacampbell@uwaterloo.ca
- regular mail:
- Sue Ann Campbell
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
N2L 3G1
Canada
This page is currently maintained by
S.A. Campbell
and was last updated on
October 13, 2009