2007

Abstract:

Dynamical systems models are commonly used to predict sizes of biological populations and to estimate the spread of pollutants. However, such models have rarely been used to examine the situation where biological species are subject to contamination of their environment. In this talk, I will outline the general problem of mercury contamination in ecosystems. Then I will give details of a dynamical systems model we are developing for predicting the amount of methylmercury contamination in aquatic food webs. The current version of the model is a system of ordinary differential equations, relating the biomass of the fish in selected trophic levels and the concentrations of mercury in these fish populations and in the environment. I will conclude by presenting preliminary results of the model.

This research is being done in collaboration with Cathy McFadyen (M.Sc. student in Environmental Science MUN) and Robin Anderson (Scientist, Fisheries and Oceans Canada), in affiliation with COMERN (the Collaborative Mercury Research Network). We are aiming to predict the methylmercury levels in food fish in specific lakes in Labrador, under various scenarios of environmental mercury loading.

Abstract:

Mathematical models for asset pricing in finance typically use a stochastic calculus approach. However, a dynamical systems modeling approach is equally valid under uncertainty, and can lead to new insights on pricing behaviour. These dynamical systems models are constructed by considering the interacting strategies of various identifiable trader groups, and result in models that are nonlinear n-dimensional maps.

In this talk, I will discuss the construction and behaviour of such models, using a relatively simple model due to Westerhoff (2005) as a specific example. I will show that the model is properly written as a nonlinear planar map, and as such can generate much interesting behaviour including global bifurcations to chaos.

This work is in collaboration with Natasha Kirby, a PhD student at Western.