## Research

**Research Area:** Applied Mathematics, Mathematical Biology

**Research Profile:** *Dynamical systems, bifurcation theory, population dynamics, mathematical ecology and epidemiology*

My students and I have been formulating and analyzing models motivated by questions in ecology and epidemiology. For example, one goal is to better understand basic population dynamics so that measurable criteria can be developed, enabling scientists to predict combinations of cultures of micro-organisms most effective and safest for use in such processes as water purification and biological waste decomposition. Other applications include pest control, the prevention of species' extinction or the control or eradication of certain diseases. In order to elicit all the potential dynamics, a bifurcation theory approach is used so that the full spectrum of behaviour can be predicted for all appropriate parameter ranges and initial states. Computer simulations are used to elucidate complicated dynamics, to test conjectures, and to reveal properties of the models that are useful in developing analytic proofs. Symbolic computation is used to carry out complicated calculations. The analyses often lead to interesting abstract mathematical problems in dynamical systems, ordinary, integro- and functional differential equations, and bifurcation theory.

Dynamical systems, bifurcation theory, population dynamics, mathematical ecology and epidemiology

## Courses

**2019/2020**

Math 1A03

Math 1ZB3

Math 741

**2018/2019**

Math 2R03

Math 3F03

Math 747

**2017/2018**

Math 2Z03

Math 3F03

Math 746

**2016/2017**

Math 2ZZ3

Math 741

**2015/2016**

Math 2Z03

Math 2ZZ3

Math 3DC3

**2014/2015**

Math 2C03

Math 741

Math 746

**2013/2014**

On Research Leave