Stability and bifurcation in interacting population models with slow-fast time scale

Stable coexistence is an important terminology in the context of interacting population models. Ordinary differential equation models of interacting populations admit two types of stable coexistence: steady-state and oscillatory. Large amplitude stable coexistence and global bifurcation of such attractors sometimes lead to extinction of one or more species. Recently, researchers are interested in understanding the large amplitude oscillation in interacting population models in the presence of a slow-fast time scale. In this talk, I will explain in detail the various kinds of oscillatory dynamics observed in interacting population models with slow-fast time scales along with the relevant terminology - canard oscillation and relaxation oscillation.