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# Population Level Phase Resetting Curves October 13, 2017 - 12:00pm Applied Mathematics Seminar

### Speaker Information

University of Pittsburgh

**Abstract**: The phase resetting tool (PRC) is a useful tool for the analysis of oscillators as it describes the effects of inputs on the phase of the oscillator. PRC theory can be used to study the synchronization between two or more oscillators as well as how oscillators entrain to periodic inputs. For the most part, PRC theory has been applied to single cells and simple systems that have stable limit cycles. However, in many biological systems (such as networks of neurons), the oscillations are a consequence of the interactions between large numbers of components, none of which may be oscillating. These are population level oscillations and observed in many systems. In this talk, (that is a collaboration with several people) we describe techniques to extend PRC theory to large networks where the oscillations emerge at the population level. This necessitates deriving the appropriate adjoint operators for systems of coupled Fokker-Planck operators. With certain types of quenched variability, we can reduce the study of the PRC to a small system of ODEs. Furthermore, we can also connect the PRCs of the network with mean-field type Wilson Cowan equations in some limits (that in practice are not to stringent). We use these methods to study entrainment of populations to periodic stimuli. If time permits, we will also discuss PRCs for oscillations that emerge in a spatial network.