Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Tuesday, 19.11.2013 17 c.t.

On the Asymptotic Phase of Stochastic Oscillators

by Prof. Peter J. Thomas
from Department of Mathematics, Case Western Reserve University, Cleveland, USA

Contact person: Fred Wolf


MPI DS seminar room (0.77/0.79)


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" is no longer well defined. I will discuss two 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) integrate-and-fire neurons with additive white noise, (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. Time permitting, I will go on to explore the interpretation of "phase resetting" in the stochastic context, and discuss connections with experimentally measured phase response distributions.

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