My students and I have been formulating and analyzing models motivated by questions in ecology. One goal is to better understand basic population dynamics so that measurable criteria can be developed, enabling scientists to predict combinations of cultures of microorganisms, most effective and safest for use in such processes as water purification and biological waste decomposition. Other applications include pest control and prevention of species' extinction. 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. Describing Nutrient Uptake, '' SIAM Journal of Applied Mathematics 45, 137-151. Bulletin of Mathematical Biology 48, 493-508. Mathematical Biosciences 83, 1-48. Coexistence and Competition Reversal,'' Mathematical Modelling in Science and Technology 8, 781-785.