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
 Keegan Keplinger (Ph.D., current)  Modelling the
Aplysia
bag cell network.
 Zhen Wang (Ph.D., current)  Neural networks with time delay and symmetry.
 Matt Kloosterman (Ph.D., current)  Plankton models with time delay.
Papers: 1.
 Wilten Nicola (Ph.D., current)  Bifurcations of networks of pulsecoupled
oscillators. Papers: 1
2
 Drew Lloyd (M.Math., May 2012)  Modelling the electrical activity of
Aplysia
bag cell neurons.
Thesis
 Raluca Jessop (Ph.D., May 2012)  Dynamics of neural systems with
distributed delays. Papers: 1
2.
Thesis
 Katie Ferguson (M.Math., August 2009)  Modelling CA1 hippocampal neurons and
astrocyte interactions. Poster
Paper
Thesis
 Ilya Kobelevskiy (M.Math., August 2008)  Type I neural oscillators with
time delayed connections.
Paper
Thesis
 Andrew Smith (M.Math., June 2007)  Phase models for FitzhughNagumo
oscillators with time delayed connections.
 Hojjat Bazzazi (M.Math, August 2005)  Synchronization in hippocampal
neural models.
Paper
Thesis
 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
Thesis
 Israel Ncube (Ph.D., May 2001)  Stochastic approximation of
artificial neural networktype learning algorithms: a dynamical
systems approach. Papers: 1
2
Thesis
 Leslie Shayer (M.Math., August 1998)  Analysis of a system
of two coupled neurons with two time delays.
Paper
Postdoctoral Researchers
 Felix Njap (January 2012  August 2014) Paper
 Muhammad DureAhmad  Large scale computational model of CA3 hippocampal
network. (November 2009  April 2011) Paper
 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
(JulyAugust 2002). Paper.
 Yuan Yuan
 Rings of neurons with delayed conections.
(JulyAugust 2002). Papers: 1
2.
 Huaiping Zhu 
Predatorprey systems/neural networks (September
1999August 2000). Paper.
Undergraduate Researchers
 Julian Kim  A conductance based model of the VD4 neuron of Lymnaea stagnalis
respiratory circuit (MayAugust 2010).
 Drew Lloyd  Modelling the ion channels of
Aplysia
bag cell neurons (MayAugust 2008, MayAugust 2009).
Photo of an Aplysia in a tidal pool.
 Steven Cheng  Implementation and analysis of an analog circuit neural
network. (JanMay 2007).
 Daniel Miller  Simulation and testing of an analog circuit
neural network. (SeptDec 2006).
 Manson Ng  Circuit representations of neural networks. (MayAugust 2006).
 Jeff Chadwick  Multistability and synchronization in neural systems.
(MayAugust 2005). Poster
 Stephanie Crawford  Control of systems with stickslip friction
(MayAugust 2005). Papers: 1
2
 Lloyd Elliott  Complex behaviour of nonautonomous maps (SeptemberDecember 2004)
 Maryam Kamgarpour  Maximizing the phase margin in the controlled,
inverted pendulum
(MayAugust 2004)
 Craig Sloss  Instability in a hybrid model for low immersion milling
(MayAugust 2002)
 Maria Landry  Controlling the delayed, inverted pendulum
(MayAugust 2000). Paper and
Videos
 Michael Waite  Coupled FitzhughNagumo neurons (MayAugust 1999).
Paper
 Simal Saujani  Degenerate double Hopf bifurcation (MayAugust 1996)
Software I use in my research
 XPPAUT (numerical integration of delay differential equations,
among other things)
 AUTO (bifurcation
continuation for ODE's)

DDEBIFTOOL (bifurcation continutation for delay differential equations)
 MATCONT (bifurcation
continuation software for ODE's that runs under Matlab.)
Online resources
Research Affiliations
Journal Affiliations
Upcoming Conferences and Workshops
Teaching
 Fall 2013
 AMATH 751  Advanced Ordinary Differential Equations

 Winter 2014
Mathematical Associations to which I belong
Math Links
Other Interests and Affiliations
How to reach me
office: MC6046
phone: (519) 8884567 Ext. 35461
fax: (519) 7464319
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