Speaker: Dr. Md Masud Rana, From the Department of Mathematics, University of Kentucky.
Abstract: Ecological stoichiometry is a framework to study population dynamics in an aquatic ecosystem that incorporates energy flow in trophic levels as well as chemical imbalances. Spatial variation in an ecological interaction also has effects on the population dynamics. We develop and analyze numerically a stoichiometric producer-grazer model in a spatially heterogeneous environment that tracks explicitly the nutrient contents. The model equations are non-linear reaction-diffusion partial differential equations. Simulations of these models produce large data sets that are difficult to analyze and interpret. We used a reduced-order modeling technique to interpret the simulation data in terms of an underlying low-dimensional dynamical system. A set of recorded “snapshot” results from the numerical simulations of the model is used to produce a reduced-order basis. Then we project the current simulation into this basis and use phase plane and bifurcation analysis to analyze the dynamics of the system.