Math Biology Seminar: Frederic Paquin-Lefebvre

When two identical nonlinear oscillators are coupled through a 1-D bulk diffusion field, new patterns of synchronization occur that would be absent in the uncoupled system. Furthermore, if the two oscillators are quiescent, the effect of the coupling can be to turn the oscillations on. Mathematically, the models consist of systems of nonlinear ODEs coupled with linear diffusive PDEs. Through a detailed bifurcation analysis of three different examples, we reveal some of the underlying mechanisms behind phenomena as diverse as the diffusion sensing of reacting agents, the synchronization of chaotic oscillations and the formation of membrane-bound patterns at the cell-scale level.