UAlberta Math Biology Seminar: Pranali Roy Chowdhury

The interactions among species in a food web or food chain are inherently complex. Mathematical models provide a framework to closely represent the dynamics observed in ecosystems. However, capturing this complexity within a single mathematical setup is extremely challenging. Biological phenomena such as growth, death, and interactions among species occur across multiple timescales. Here, I will demonstrate the importance of a multiscale framework in mathematical modelling to study the dynamics of interacting species. By applying geometric singular perturbation and blow-up theory, I will discuss the existence of canards and relaxation oscillations in ecological models, and illustrate how the entry-exit function helps in determining critical thresholds associated with sudden transitions in population density. I will illustrate how incorporating diverse timescales into mathematical models can provide new insights into capturing the large amplitude periodic fluctuations observed in ecosystems. Further, I will discuss how slow-fast systems can help in understanding the long transients observed in the ecological datasets.