(With: Gaurav Raina, Ramya Korlakai Vinayak)

Biological systems are ripe with phenomenon occurring across various timescales, yet conventional system design principles steer us away from the very phenomena that make biology interesting. It is not obvious that conventional design wisdom applies in this setting. We shed some light on the topic through the study of two of the simplest quadratic population models with two distinct timescales. We show that they capture the range of phenomenon from fixed points, to limit cycles, to chaos, and analytically characterise the same using Hopf bifurcation theory. We comment on the qualitative differences between the two models, and the resulting implications to control theory.

• This project began as part of a course in non-linear analysis. The final submitted report can be found here.
• We are currently working on a submission to SIAM SIADS.