QUANTITATIVE BIOLOGY SEMINAR<br>Keeping the Beat: Homeostatic Frequency Control in Coupled Oscillators

When nonlinear oscillators are forced or coupled they will generally lock if the frequency is in a narrow enough range. However, humans and other animals such as fireflies and Snowball the dancing cockatoo are able to adjust the intrinsic frequency of their oscillators to widen the range of locking and zeroing the phase-lag. In this talk, I will start with some simple abstract circle maps and show that when the frequency is modulated by the coupling there are many possible final states and fractal basin boundaries between them. I will then turn to continuous time oscillators. Using averaging I will derive a new class of phase models and analyze their properties. I apply this to some neural models and show how the homeostatic control of the frequency greatly expands the ability to lock. Finally, I show that traveling periodic wave trains can be destabilized in the when there is frequency adjustment in rings of coupled oscillators.