Mathias Heltberg

The purpose of this visit was to further a collaboration between the groups of Mogens Jensen (a previous Simons visitor), Sanjay Sane (NCBS) and Sandeep Krishna. The project involves the experimental study, in Sanjay Sane's lab, of coupled oscillators involved in insect flight and theoretical modelling of such coupled oscillators by Mathias, supervised by Mogens Jensen and Sandeep Krishna. The insect wing and the haltere are the two oscillators that are mechanically coupled through the insect body. In normal flies, the coupling causes the two structures to synchronize and oscillate out of phase. Theoretical analysis of coupled oscillators predicts the presence of finite windows of synchronization, called Arnold tongues, as the frequency of one of the oscillators is varied. And this is indeed observed by Tanvi Deora, Sanjay Sane's student, when she increases the frequency of the wing by clipping portions off. The project has two aims: (i) to use mathematical models to understand the nature of nonlinearities in the insect oscillators and their couplings, (ii) to discover new physics in coupled oscillators because the biological system works in a parameter regime which is not at all well understood, where Arnold tongues start overlapping.