Speaker
Description
Two identical oscillators with mutual inhibition provide a conceptual framework for modeling a latching mechanism in cell cycle regulation. In this talk, we study two such coupled oscillator models and investigate mechanisms of symmetry-breaking. In both models, inhibitory coupling induces stable alternating large-amplitude oscillations corresponding to the normal cell cycle. However, the systems also exhibit strong symmetry-breaking states in which the two oscillators display qualitatively different rhythms. In one case, this corresponds to endocycles, in which only one of the two oscillators undergoes large-amplitude oscillations. Using bifurcation analysis and geometric singular perturbation theory, we identify and characterize two distinct strong symmetry-breaking mechanisms: one arising through a homoclinic bifurcation and the other through a novel type of symmetric folded singularity.
