Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Nonlinear stochastic systems

DY 30.10: Talk

Friday, March 27, 2009, 12:30–12:45, ZEU 118

Interspike Interval Correlations of a Nonrenewal Integrate-and-Fire Neuron — •Tilo Schwalger, Rafael Dias Vilela, and Benjamin Lindner — MPI PKS, Dresden

Spike trains of neurons are often characterized by the interspike interval (ISI) density or even simpler by its first two moments (corresponding to firing rate and coefficient of variation). This first-order statistics is sufficient if the spike train constitutes a renewal point process, i.e. if all ISI's are statistically independent. It has been found, however, that ISI's of cortical neurons are correlated and hence nonrenewal, and it has been argued that such higher-order statistics of spike trains could be tightly related to biological functions, as e.g. spike frequency adaptation. In an integrate-and-fire neuron model such ISI correlations could be the result of a temporally correlated driving (synaptic input) or a threshold dynamics.

In this work we present an analytical technique to calculate the serial correlation coefficient (SCC) for an excitable integrate-and-fire neuron that is driven by a telegraph process (dichotomous noise) and white noise. The method is based on a discrete kinetic description and within this framework all results are exact. For slow driving we find a large, positive SCC, which has a maximum at a finite driving amplitude. As special cases the theoretical framework also includes simple threshold dynamics and residence time correlations of driven bistable systems.

Reference: T. Schwalger and B. Lindner, Phys. Rev. E 78, 021121, 2008