CMMB Seminar: On the Asymptotic Phase of Stochastic Oscillators

Speaker: Peter Thomas, Case Western Reserve University, Ohio, USA.

Title: On the Asymptotic Phase of Stochastic Oscillators

Abstract:

The synchronization, entainment, and information processing properties of spontaneously firing nerve cells may be understood in terms of the infinitesimal phase response curve (iPRC) of neural oscillator models.The iPRC quantifies the shift in the timing of an oscillation in response to a small, brief input. For deterministic dynamical models the iPRC is defined in terms of the oscillator's asymptotic phase function. For stochastic dynamical models, the usual definition of the iPRC breaks down, because in the presence of even small amounts of noise, the "asymptotic phase" of an oscillator is no longer well defined. I will discuss alternative approaches to redefining the"asymptotic phase" of an oscillator, in a way that is consistent across both the stochastic and deterministic settings. As examples, I will consider three increasingly realistic classes of models: (1) a noise-dependent oscillator for which the underlying deterministic dynamical system does not have a finite period limit cycle (2) Gaussian stochastic differential equation models derived from conductance-based systems of ordinary differential equations, and (3) hybrid jump Markov process models, in which random ion channel gating is represented as a discrete time-inhomogeneous Markov process, and the voltage dynamics are conditionally deterministic.