Manchester Applied Mathematics and Numerical Analysis Seminars Winter 1998

October 14, 1998, 2.30 pm

Lecture Theatre D13 Material Science

Dynamics from interspike intervals

Dr. Natalia Janson, Saratov

Many kinds of physical processes, especially physiological ones such as electro-cardiograms, yield data in the form of a series of intervals between events: interspike intervals (ISI). In this talk I will discuss two classes of processes that generate spikes: integrate-and-fire models and threshold-crossing ones. I will also explore ways to analyse time series of interspike intervals, beginning with Tim Sauer's theorem about the methods of delays (aka Ruelle-Takens embedding) as applied to integrate-and-fire models.

I will talk about three ways introduce a phase for such systems and so to define an instantaneous frequency. This will lead to a discussion of threshold-crossing ISI systems and their connection with instantaneous frequency, Poincare maps and return-time maps. Next, I will show how to extract various dynamical invariants of a threshold-crossing ISI's underlying dynamical system, including its dimension and Lyapunov exponents. And finally, I apply the method to a real signal from the cardiovascular system of a human, namely, to the sequence of RR-intervals.

For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).